# On Shapiro's lethargy theorem and some applications

@inproceedings{Aksoy2012OnSL, title={On Shapiro's lethargy theorem and some applications}, author={Asuman G{\"u}ven Aksoy and Jos{\'e} Mar{\'i}a Almira}, year={2012} }

Shapiro’s lethargy theorem [48] states that if {An} is any non-trivial linear approximation scheme on a Banach space X ,t hen the sequences of errors of best approximation E(x,An )=i nfa∈An ∥x − an∥X may decay almost arbitrarily slowly. Recently, Almira and Oikhberg [11, 12] 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 .W e also provide applications to the…

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