Artículo
Some properties and applications of equicompact sets of operators
Autor/es | Enrique Serrano Aguilar
Cándido Piñeiro Gómez Juan Manuel Delgado Sánchez |
Departamento | Departamento de Matemática Aplicada I |
Fecha de publicación | 2007 |
Fecha de depósito | 2020-05-08 |
Resumen | 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 ... 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. |
Cita | Enrique Serrano Aguilar, , Cándido Piñeiro Gómez, y Juan Manuel Delgado Sánchez, (2007). Some properties and applications of equicompact sets of operators. Studia Mathematica, 181 (2), 171-180. |
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