Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607078 | Journal of Approximation Theory | 2014 | 18 Pages |
Abstract
We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given ε>0ε>0, so that the basis becomes (1+ε)(1+ε)-democratic, and hence (2+ε)(2+ε)-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is (1+ε)(1+ε)-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in Lp[0,1]Lp[0,1], 1
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
S.J. Dilworth, D. Kutzarova, E. Odell, Th. Schlumprecht, A. Zsák,