Grothendieck's theorem for noncommutative C-algebras, with an Appendix on Grothendieck's constants Academic Article uri icon

abstract

  • We study a conjecture of Grothendieck on bilinear forms on a C*-algebra Ol. We prove that every "approximable" operator from Ol into Ol* factors through a Hilbert space, and we describe the factorization. In the commutative case, this is known as Grothendieck's theorem. These results enable us to prove a conjecture of Ringrose on operators on a C*-algebra. In the Appendix, we present a new proof of Grothendieck's inequality which gives an improved upper bound for the so-called Grothendieck constant kG. 1978.

published proceedings

  • Journal of Functional Analysis

altmetric score

  • 11.552

author list (cited authors)

  • Pisier, G.

citation count

  • 80

complete list of authors

  • Pisier, Gilles

publication date

  • September 1978