Shapiro's Theorem for subspaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Almira, J. M.¹  Oikhberg, T.^2,3 

[1] Univ Jaen, Dept Matemat, EPS Linares, Linares 23700, Jaen, Spain

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

关键词: Approximation scheme;    Approximation error;    Approximation with restrictions;    Bernstein's Lethargy Theorem;    Shapiro's Theorem;   

DOI  :  10.1016/j.jmaa.2011.09.054

来源: Elsevier

【 摘 要 】

In the previous paper (Almira and Oikhberg. 2010 [4]), the authors investigated the existence of an element x of a quasi-Banach space X whose errors of best approximation by a given approximation scheme (A(n)) (defined by E(x, A(n)) = inf(a is an element of An) parallel to x - a(n)parallel to) decay arbitrarily slowly. In this work, we consider the question of whether x witnessing the slowness rate of approximation can be selected in a prescribed subspace of X. In many particular cases, the answer turns out to be positive. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free