HR job title
- Retired Distinguished Professor
- Contact Info
- 1 979 845 7278
Pisier, Gilles Distinguished Professor
Positions
- Distinguished Professor, Mathematics, College of Arts and Sciences
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
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Overview
Publications
selected publications
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academic article
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Pisier, G.
(2020).
A non-nuclear C*-algebra with the weak expectation property and the local lifting property. Inventiones Mathematicae.
222(2), 513-544.
-
Pisier, G.
(2019).
On a Characterization of the Weak Expectation Property (WEP)
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Pisier, G.
(2019).
A Note on Sidon Sets in Bounded Orthonormal Systems. Journal of Fourier Analysis and Applications.
25(3), 995-1007.
-
Pisier, G.
(2018).
Completely Sidon sets in C*-algebras. Monatshefte fuer Mathematik.
187(2), 357-374.
-
Pisier, G.
(2018).
On a linearization trick. 64(3-4), 315-326.
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Naor, A., Pisier, G., & Schechtman, G.
(2018).
Impossibility of dimension reduction in the nuclear norm. 1345-1352.
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Pisier, G.
(2018).
Spectral Gap Properties of the Unitary Groups: Around Riders Results on Non-commutative Sidon Sets. Operator Theory Advances and Applications.
261, 417-465.
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Pisier, G., & Ricard, E.
(2017).
THE NON-COMMUTATIVE KHINTCHINE INEQUALITIES FOR 0 < p < 1. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU.
16(5), 1103-1123.
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Pisier, G.
(2017).
On uniformly bounded orthonormal Sidon systems. Mathematical Research Letters.
24(3), 893-932.
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Pisier, G.
(2016).
Strong convergence for reduced free products. Infinite Dimensional Analysis Quantum Probability and Related Topics.
19(2), 1650008-1650008.
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Ozawa, N., & Pisier, G.
(2016).
A CONTINUUM OF C*-NORMS ON B(H) circle times (H) AND RELATED TENSOR PRODUCTS. Glasgow Mathematical Journal.
58(2), 433-443.
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Pisier, G.
(2015).
Quantum expanders and growth of group representations. Annales- Faculte des Sciences Toulouse Mathematiques.
26(2), 451-462.
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Pisier, G.
(2015).
ON THE METRIC ENTROPY OF THE BANACH-MAZUR COMPACTUM. Mathematika: a journal of pure and applied mathematics.
61(1), 179-198.
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Pisier, G.
(2014).
RANDOM MATRICES AND SUBEXPONENTIAL OPERATOR SPACES. Israel Journal of Mathematics.
203(1), 223-273.
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Pisier, G.
(2014).
MARTINGALE INEQUALITIES AND OPERATOR SPACE STRUCTURES ON L-p. DOCUMENTA MATHEMATICA.
19(2014), 1367-1442.
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Pisier, G.
(2014).
Quantum expanders and geometry of operator spaces. Journal of the European Mathematical Society.
16(6), 1183-1219.
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Pisier, G.
(2013).
Real interpolation and transposition of certain function spaces. Revista Matematica Complutense.
26(1), 89-97.
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Pisier, G.
(2012).
COMPLETELY CO-BOUNDED SCHUR MULTIPLIERS. Operators and Matrices.
6(2), 263-270.
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Pisier, G.
(2012).
GROTHENDIECK'S THEOREM, PAST AND PRESENT. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
49(2), 237-323.
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Pisier, G.
(2011).
Real Interpolation between Row and Column Spaces. 59(3), 237-259.
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Pisier, G.
(2011).
Random Series of Trace Class Operators
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Pisier, G.
(2010).
Complex Interpolation between Hilbert, Banach and Operator Spaces. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY.
208(978), 1-+.
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Pisier, G.
(2009).
Remarks on the non-commutative Khintchine inequalities for 0 < p < 2. Journal of Functional Analysis.
256(12), 4128-4161.
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Pisier, G.
(2007).
A Remark on Hypercontractive Semigroups and Operator Ideals
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Grigorchuk, R., Pisier, G., & uni, Z.
(2007).
Geometriae Dedicata: Preface. Geometriae Dedicata.
124(1), 1-4.
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Pisier, G.
(2007).
Simultaneous similarity, bounded generation and amenability. TOHOKU MATHEMATICAL JOURNAL.
59(1), 79-99.
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Pisier, G.
(2006).
A similarity degree characterization of nuclear C*-algebras. Publications of the Research Institute for Mathematical Sciences.
42(3), 691-704.
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Parcet, J., & Pisier, G.
(2005).
Non-commutative Khintchine type inequalities associated with free groups. INDIANA UNIVERSITY MATHEMATICS JOURNAL.
54(2), 531-556.
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Pisier, G.
(2005).
Are Unitarizable Groups Amenable?. Progress in Mathematics.
248, 323-362.
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Pisier, G.
(2004).
Completely bounded maps into certain Hilbertian operator spaces. International Mathematics Research Notices.
2004(74), 3983-4018.
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Narcowich, F. J., & Ward, J. D.
(2004).
Preface. Advances in Computational Mathematics.
21(1-2), 1-2.
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Pisier, G.
(2004).
The operator Hilbert space OH and type III von Neumann algebras. Bulletin of the London Mathematical Society.
36(4), 455-459.
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Pisier, G., & Shlyakhtenko, D.
(2002).
Grothendieck's theorem for operator spaces. Inventiones Mathematicae.
150(1), 185-217.
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Nazarov, F., Pisier, G., Treil, S., & Volberg, A.
(2002).
Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
542(542), 147-171.
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Pisier, G.
(2001).
Remarks on the similarity degree of an operator algebra. International Journal of Mathematics.
12(4), 403-414.
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Pisier, G.
(2001).
Multipliers of the Hardy space H 1 and power bounded operators. Colloquium Mathematicum.
88(1), 57-73.
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Pisier, G.
(2001).
Similarity problems and length. Taiwanese Journal of Mathematics.
5(1), 1-17.
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Pisier, G.
(2000).
An inequality for p-orthogonal sums in non-commutative L-p. Illinois Journal of Mathematics.
44(4), 901-923.
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Pisier, G.
(2000).
The similarity degree of an operator algebra, II. Mathematische Zeitschrift.
234(1), 53-81.
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Oikhberg, T., & Pisier, G.
(1999).
The "maximal" tensor product of operator spaces. Proceedings of the Edinburgh Mathematical Society.
42(2), 267-284.
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Pisier, G.
(1998).
Non-commutative vector valued L-p-spaces and completely p-summing maps - Introduction. ASTERISQUE.
247(247), 1-+.
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Pisier, G.
(1998).
Joint similarity problems and the generation of operator algebras with bounded length. Integral Equations and Operator Theory.
31(3), 353-370.
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Pisier, G.
(1997).
Espaces d'oprateurs: Une nouvelle dualit. ASTERISQUE.
241, 243-272.
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Pisier, G.
(1997).
Quadratic forms in unitary operators. Linear Algebra and Its Applications.
267(1-3), 125-137.
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Pisier, G.
(1997).
A polynomially bounded operator on Hilbert space which is not similar to a contraction. Journal of the American Mathematical Society.
10(2), 351-369.
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Pisier, G., & Xu, Q. H.
(1997).
Non-commutative Martingale inequalities. Communications in Mathematical Physics.
189(3), 667-698.
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Pisier, G.
(1997).
Operator spaces: A new duality. ASTERISQUE.
243-272.
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Pisier, G.
(1997).
The degree of similarity of an operator algebra. Comptes Rendus Mathematique (Academie des Sciences).
324(3), 287-292.
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Pisier, G.
(1996).
A simple proof of a theorem of kirchberg and related results on C*-norms. Journal of Operator Theory.
35(2), 317-335.
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Pisier, G.
(1996).
Dvoretzky's theorem for operator spaces. HOUSTON JOURNAL OF MATHEMATICS.
22(2), 399-416.
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Pisier, G.
(1996).
The operator Hilbert space OH, complex interpolation and tensor norms. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY.
122(585), 1-&.
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Pisier, G.
(1996).
A polynomially bounded operator on Hilbert space which is not similar to a contraction. Comptes Rendus Mathematique (Academie des Sciences).
322(6), 547-550.
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Pisier, G., & Xu, Q. H.
(1996).
Non-commutative martingale inequalities. Comptes Rendus Mathematique (Academie des Sciences).
323(7), 817-822.
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HESS, A., & PISIER, G.
(1995).
THE K-T-FUNCTIONAL FOR THE INTERPOLATION COUPLE L(INFINITY)(D-MU, L(1)(DV)), L(INFINITY)(DV, L(1)(D-MU)). Quarterly Journal of Mathematics.
46(183), 333-344.
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Pisier, G.
(1995).
Exact operator spaces. ASTERISQUE.
159-&.
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JUNGE, M., & PISIER, G.
(1995).
BILINEAR-FORMS ON EXACT OPERATOR-SPACES AND B(H)CIRCLE-TIMES-B(H). GEOMETRIC AND FUNCTIONAL ANALYSIS.
5(2), 329-363.
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Pisier, G.
(1995).
Projections from a von Neumann algebra onto a subalgebra. Bulletin de la Societe Mathematique de France.
123(1), 139-153.
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PISIER, G.
(1995).
MULTIPLIERS AND LACUNARY SETS IN NON-AMENABLE GROUPS. American Journal of Mathematics.
117(2), 337-376.
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PISIER, G.
(1994).
COMPLEX INTERPOLATION AND REGULAR OPERATORS BETWEEN BANACH-LATTICES. Archiv der Mathematik.
62(3), 261-269.
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HAAGERUP, U., & PISIER, G.
(1993).
BOUNDED LINEAR-OPERATORS BETWEEN C-ASTERISK-ALGEBRAS. DUKE MATHEMATICAL JOURNAL.
71(3), 889-925.
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PISIER, G.
(1993).
THE KT-FUNCTIONAL FOR THE INTERPOLATION COUPLE L(1)(A(0)), L(INFINITY)(A(1)). Journal of Approximation Theory.
73(1), 106-117.
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PISIER, G.
(1993).
OPERATORS FACTORIZABLE THROUGH OH. Comptes Rendus Mathematique (Academie des Sciences).
316(2), 165-170.
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PISIER, G.
(1993).
THE OPERATOR HILBERT-SPACE AND COMPLEX INTERPOLATION. Comptes Rendus Mathematique (Academie des Sciences).
316(1), 47-52.
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PISIER, G.
(1992).
FACTORIZATION OF OPERATOR VALUED ANALYTIC-FUNCTIONS. Advances in Mathematics.
93(1), 61-125.
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PISIER, G.
(1992).
A SIMPLE PROOF OF A THEOREM OF BOURGAIN,JEAN. MICHIGAN MATHEMATICAL JOURNAL.
39(3), 475-484.
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Pisier, G.
(1992).
A simple proof of a theorem of Jean Bourgain. MICHIGAN MATHEMATICAL JOURNAL.
39(3), 475-484.
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PISIER, G.
(1992).
INTERPOLATION BETWEEN HP SPACES AND NONCOMMUTATIVE GENERALIZATIONS .1. PACIFIC JOURNAL OF MATHEMATICS.
155(2), 341-368.
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PISIER, G.
(1992).
REMARKS ON COMPLEMENTED SUBSPACES OF VONNEUMANN-ALGEBRAS. Proceedings of the Royal Society of Edinburgh Section A Mathematics.
121(1-2), 1-4.
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LUSTPIQUARD, F., & PISIER, G.
(1991).
NONCOMMUTATIVE KHINTCHINE AND PALEY INEQUALITIES. Arkiv foer Matematik.
29(2), 241-260.
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JOHNSON, W. B., & PISIER, G.
(1991).
THE PROPORTIONAL UAP CHARACTERIZES WEAK HILBERT-SPACES. Journal of London Mathematical Society.
44(3), 525-536.
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PISIER, G.
(1990).
A REMARK ON PI-2(LP,LP). Mathematische Nachrichten.
148, 243-245.
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PISIER, G.
(1990).
COMPLETELY BOUNDED MAPS BETWEEN SETS OF BANACH-SPACE OPERATORS. INDIANA UNIVERSITY MATHEMATICS JOURNAL.
39(1), 249-277.
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PISIER, G.
(1989).
A NEW APPROACH TO SEVERAL RESULTS OF MILMAN,V. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
393(393), 115-131.
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PISIER, G.
(1988).
FACTORIZATION OF OPERATOR VALUED ANALYTIC-FUNCTIONS. Comptes Rendus Mathematique (Academie des Sciences).
307(19), 955-960.
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PISIER, G., & XU, Q. H.
(1988).
THE STRONG P-VARIATION OF MARTINGALES AND ORTHOGONAL SERIES. Probability Theory and Related Fields.
77(4), 497-514.
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PISIER, G.
(1988).
THE DUAL J-STAR OF THE JAMES SPACE HAS COTYPE-2 AND THE GORDON-LEWIS PROPERTY. Cambridge Philosophical Society: Mathematical Proceedings.
103(2), 323-331.
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PISIER, G.
(1988).
WEAK HILBERT-SPACES. Proceedings of the London Mathematical Society.
56(3), 547-579.
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MILMAN, V. D., & PISIER, G.
(1987).
GAUSSIAN-PROCESSES AND MIXED VOLUMES. Annals of Probability.
15(1), 292-304.
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MILMAN, V. D., & PISIER, G.
(1986).
BANACH-SPACES WITH A WEAK COTYPE-2 PROPERTY. Israel Journal of Mathematics.
54(2), 139-158.
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PISIER, G.
(1986).
FACTORIZATION OF OPERATORS THROUGH L-INFINITY, OR LP-1 AND NONCOMMUTATIVE GENERALIZATIONS. Mathematische Annalen.
276(1), 105-136.
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PISIER, G.
(1986).
PROBABILISTIC METHODS IN THE GEOMETRY OF BANACH-SPACES. Lecture Notes in Mathematics.
1206, 167-241.
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MARCUS, M. B., & PISIER, G.
(1985).
STOCHASTIC-PROCESSES WITH SAMPLE PATHS IN EXPONENTIAL ORLICZ SPACES. Lecture Notes in Mathematics.
1153, 329-358.
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MARCUS, M. B., & PISIER, G.
(1984).
CHARACTERIZATIONS OF ALMOST SURELY CONTINUOUS P-STABLE RANDOM FOURIER-SERIES AND STRONGLY STATIONARY-PROCESSES. Acta Mathematica.
152(3-4), 245-301.
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PISIER, G.
(1983).
COUNTEREXAMPLES TO A CONJECTURE OF GROTHENDIECK. Acta Mathematica.
151(3-4), 181-208.
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Bourgain, J., & Pisier, G.
(1983).
A construction of -spaces and related Banach spacesand related Banach spaces. Boletim da Sociedade Brasileira de Matematica: Nova Serie.
14(2), 109-123.
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PISIER, G.
(1983).
ON THE DIMENSION OF THE LPN-SUBSPACES OF BANACH-SPACES, FOR 1 LESS-THAN-OR-EQUAL-TO P LESS-THAN 2. Transactions of the American Mathematical Society.
276(1), 201-211.
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Pisier, G.
(1983).
On the dimension of the l p n l^{n}_{p} -subspaces of Banach spaces, for 1 p < 2 1leq p<2. Transactions of the American Mathematical Society.
276(1), 201-211.
-
PISIER, G.
(1983).
SOME APPLICATIONS OF THE METRIC ENTROPY CONDITION TO HARMONIC-ANALYSIS. Lecture Notes in Mathematics.
995, 123-154.
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PISIER, G.
(1983).
ARITHMETIC CHARACTERIZATIONS OF SIDON SETS. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
8(1), 87-89.
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PISIER, G.
(1982).
HOLOMORPHIC SEMIGROUPS AND THE GEOMETRY OF BANACH-SPACES. Annals of Mathematics.
115(2), 375-392.
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PISIER, G.
(1982).
QUOTIENTS OF BANACH-SPACES OF COTYPE-Q. Proceedings of the American Mathematical Society.
85(1), 32-36.
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Pisier, G.
(1982).
Quotients of Banach spaces of cotype q q. Proceedings of the American Mathematical Society.
85(1), 32-36.
-
PISIER, G.
(1979).
SOME APPLICATIONS OF THE COMPLEX INTERPOLATION METHOD TO BANACH-LATTICES. Journal d'Analyse Mathematique.
35(1), 264-281.
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PISIER, G.
(1979).
REMARKABLE HOMOGENEOUS BANACH ALGEBRA. Israel Journal of Mathematics.
34(1-2), 38-44.
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PISIER, G., & ZINN, J.
(1978).
LIMIT-THEOREMS FOR RANDOM-VARIABLES WITH VALUES IN SPACES LP (2LESS-THAN-OR-EQUAL-TO P LESS-THAN INFINITY). Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete.
41(4), 289-304.
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PISIER, G.
(1978).
GROTHENDIECK THEOREM FOR NONCOMMUTATIVE CSTAR-ALGEBRAS, WITH AN APPENDIX ON GROTHENDIECK CONSTANTS. Journal of Functional Analysis.
29(3), 397-415.
-
HOFFMANNJORGENSEN, J., & PISIER, G.
(1976).
LAW OF LARGE NUMBERS AND CENTRAL LIMIT-THEOREM IN BANACH-SPACES. Annals of Probability.
4(4), 587-599.
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PISIER, G.
(1975).
MARTINGALES WITH VALUES IN UNIFORMLY CONVEX-SPACES. Israel Journal of Mathematics.
20(3-4), 326-350.
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Enflo, P., Lindenstrauss, J., & Pisier, G.
(1975).
On the "Three space problem". Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci.
36, 199-210.
-
Pisier, G.
Quantum Expanders and Geometry of Operator Spaces II
-
Pisier, G.
(2020).
A non-nuclear C*-algebra with the weak expectation property and the local lifting property. Inventiones Mathematicae.
222(2), 513-544.
-
book
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Pisier, G.
(2016).
Martingales in Banach Spaces. Cambridge University Press (CUP).
-
Pisier, G.
(2003).
Introduction to Operator Space Theory. Cambridge University Press (CUP).
-
Pisier, G.
(1996).
Similarity Problems and Completely Bounded Maps. Ed. 1618.
Springer Nature.
-
Pisier, G.
(1989).
The Volume of Convex Bodies and Banach Space Geometry. Cambridge University Press (CUP).
-
Pisier, G.
(1986).
Factorization of Linear Operators and Geometry of Banach Spaces. Ed. 60.
American Mathematical Society (AMS).
-
MARCUS, M. B., & PISIER, G.
(1981).
RANDOM FOURIER-SERIES WITH APPLICATIONS TO HARMONIC-ANALYSIS. Princeton University Press.
-
Pisier, G.
(2016).
Martingales in Banach Spaces. Cambridge University Press (CUP).
-
chapter
-
Davis, B., & Song, R.
(2011).
Don Burkholders work on Banach spaces. Davis, B., & Song, R. (Eds.),
Selected Works of Donald L. Burkholder.
(pp. 23-30).
Springer Nature.
-
Pisier, G.
(2010).
The Halmos Similarity Problem. Operator Theory Advances and Applications.
Axler, S., Rosenthal, P., & Sarason, D. (Eds.),
GLIMPSE AT HILBERT SPACE OPERATORS.
(pp. 325-339).
Springer Nature.
-
Pisier, G.
(2003).
Chapter 33 Operator Spaces. Handbook of the Geometry of Banach Spaces.
Handbook of the Geometry of Banach Spaces.
(pp. 1425-1458).
Elsevier.
-
Pisier, G., & Xu, Q.
(2003).
Chapter 34 Non-Commutative Lp-Spaces. Handbook of the Geometry of Banach Spaces.
Handbook of the Geometry of Banach Spaces.
(pp. 1459-1517).
Elsevier.
-
PISIER, G.
(1982).
ON THE DUALITY BETWEEN TYPE AND COTYPE. Lecture Notes in Mathematics.
Chao, J., & Woyczyński, W. A. (Eds.),
Martingale Theory in Harmonic Analysis and Banach Spaces.
(pp. 131-144).
Springer Nature.
-
Davis, B., & Song, R.
(2011).
Don Burkholders work on Banach spaces. Davis, B., & Song, R. (Eds.),
Selected Works of Donald L. Burkholder.
(pp. 23-30).
Springer Nature.
-
conference paper
-
Pisier, G.
(2006).
Remarks on B(H) circle times B(H). Proceedings: Mathematical Sciences.
423-428.
-
Fonf, V. P., Johnson, W. B., Pisier, G., & Preiss, D.
(2003).
Stochastic approximation properties in Banach spaces. Studia Mathematica.
103-119.
-
Pisier, G.
(2006).
Remarks on B(H) circle times B(H). Proceedings: Mathematical Sciences.
423-428.
Research
co-principal investigator on
- Workshop in Analysis and Probability awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2020
- Workshop in Analysis and Probability awarded by National Science Foundation - (Arlington, Virginia, United States) 2015 - 2019
- Conference: Geometric and Probabilistic Methods in Group Theory and Dynamical Systems awarded by National Science Foundation - (Arlington, Virginia, United States) 2015 - 2016
- NSF-Workshop In Analysis and Probability awarded by National Science Foundation - (Arlington, Virginia, United States) 2012 - 2016
Teaching
teaching activities
- MATH663 Seminar In Analysis Instructor
Works By Students
chaired theses and dissertations
-
Iushchenko, Kateryna (2012-02). On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w.
-
Kravchenko, Rostyslav (2011-02). Measure Theory of Self-Similar Groups and Digit Tiles.
-
Mei, Tao (2006-10). Operator valued Hardy spaces and related subjects.
Background
education and training
- Ph.D. in Mathematics, Paris Diderot University - (Paris, France) 1977
awards and honors
- Fellow, conferred by American Mathematical Society - (Providence, Rhode Island, United States), 2013
- Stefan Banach Medal, conferred by Polish Academy of Sciences - (Warsaw, Poland), 2001
- University Professorships for Undergraduate Teaching Excellence, conferred by Texas A&M University - (College Station, Texas, United States), 1998
- Fellow, conferred by Institute of Mathematical Statistics - (Beachwood, Ohio, United States), 1989
Contact
first name
- Gilles
has last name
- Pisier
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- pisier@tamu.edu