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arXiv · 1211.3356

On Shapiro's lethargy theorem and some applications

A. G. Aksoy·J. M. Almira
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Abstract

Shapiro's lethargy theorem states that if {A_n} is any non-trivial linear approximation scheme on a Banach space X, then the sequences of errors of best approximation E(x,A_n) = \inf_{a \in A_n} ||x - a_n||_X decay almost arbitrarily slowly. Recently, Almira and Oikhberg investigated this kind of result for general approximation schemes in the quasi-Banach setting. In this paper, we consider the same question for F-spaces with non decreasing metric d. We also provide applications to the rate of decay of s-numbers, entropy numbers, and slow convergence of sequences of operators.

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A. G. Aksoy, J. M. Almira. 2013-09-19. On Shapiro's lethargy theorem and some applications. https://arxiv.org/abs/1211.3356

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