Renormings and symmetry properties of 1-greedy bases Academic Article uri icon

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

author list (cited authors)

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

citation count

  • 4

publication date

  • September 2011