Renormings and symmetry properties of 1-greedy bases

abstract

• We continue the study of 1-greedy bases initiated by Albiac and Wojtaszczyk (2006) [1]. We answer several open problems that they raised concerning symmetry properties of 1-greedy bases and the improving of the greedy constant by renorming. We show that 1-greedy bases need not be symmetric or subsymmetric. We also prove that one cannot in general make a greedy basis 1-greedy as demonstrated for the Haar basis of the dyadic Hardy space H1(R) and for the unit vector basis of Tsirelson space. On the other hand, we give a renorming of Lp (1

authors

• Schlumprecht, Thomas

published proceedings

• Journal of Approximation Theory

author list (cited authors)

• Dilworth, S. J., Odell, E., Schlumprecht, T. h., & Zsk, A.

citation count

• 6

complete list of authors

• Dilworth, SJ||Odell, E||Schlumprecht, Th||Zsák, A

publication date

• January 2011

publisher

• Elsevier  Publisher

published in

• Journal of Approximation Theory  Journal

Digital Object Identifier (DOI)

• 10.1016/j.jat.2011.02.013

start page

• 1049

end page

• 1075

volume

• 163

issue

• 9

URL

• http://dx.doi.org/10.1016/j.jat.2011.02.013