Some properties and applications of equicompact sets of operators
Let X and Y be Banach spaces. A subset M of K(X,Y ) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xn) in X has a subsequence (xk(n))n such that (Txk(n))n is uniformly convergent for T ∈ M. We study the re...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/96304 |
| Acceso en línea: | https://hdl.handle.net/11441/96304 https://doi.org/10.4064/sm181-2-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Compact operators Equicompact sets of operators Collectively compact set Vector measures Ascoli’s theorem |
| Sumario: | Let X and Y be Banach spaces. A subset M of K(X,Y ) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xn) in X has a subsequence (xk(n))n such that (Txk(n))n is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion in Mc(F,X), the Banach space of all (finitely additive) vector measures (with compact range) from a field F of sets into X endowed with the semivariation norm. |
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