On Shapiro’s lethargy theorem and some applications

• Autores: Asuman Güven Aksoy, José María Almira Picazo
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 6, Nº. 1, 2014, págs. 87-116
• Idioma: inglés
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• Resumen

  • Shapiro’s lethargy theorem (48) states that if {An} is any non-trivial linear approximation scheme on a Banach space X, then the sequences of errors of best approximation E(x, An) = infₐ∈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. We also provide applications to the rate of decay of s-numbers, entropy numbers and slow convergence of sequences of operators.