On Shapiro’s lethargy theorem and some applications
- Asuman G. Aksoy
- José M. Almira
ISSN: 1889-3066, 1989-7251
Any de publicació: 2014
Volum: 6
Número: 1
Pàgines: 87-116
Tipus: Article
Altres publicacions en: Jaen journal on approximation
Resum
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.