Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607160 | Journal of Approximation Theory | 2014 | 11 Pages |
Abstract
We show that none of the spaces (⨁n=1∞ℓp)ℓq, 1≤p≠q<∞1≤p≠q<∞ have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprecht. Similarly, the spaces (⨁n=1∞ℓp)c0, 1≤p<∞1≤p<∞, and (⨁n=1∞co)ℓq, 1≤q<∞1≤q<∞, do not have greedy bases. It follows from that and known results that a class of Besov spaces on RnRn lack greedy bases as well.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gideon Schechtman,