No greedy bases for matrix spaces with mixed lp and lq norms

JOURNAL OF APPROXIMATION THEORY

卷:184

Article

Schechtman, Gideon

关键词: Greedy basis;    Matrix spaces;    Besov spaces;   

DOI  :  10.1016/j.jat.2014.05.004

来源: Elsevier

【 摘 要 】

We show that none of the spaces (circle plus(infinity)(n=1) l(p))l(q), 1 <= p not equal q < infinity have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprecht. Similarly, the spaces (circle plus(infinity)(n=1) l(p))c(0), 1 <= B < infinity, and (circle plus(infinity)(n=1) c(0))l(q), 1 <= q < infinity, do not have greedy bases. It follows from that and known results that a class of Besov spaces on Rn lack greedy bases as well. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free