Article ID Journal Published Year Pages File Type
4607160 Journal of Approximation Theory 2014 11 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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