Renormings and symmetry properties of 1-greedy bases
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We continue the study of 1-greedy bases initiated by Albiac and Wojtaszczyk (2006) . 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.