Let X and Y be Banach spaces. A subset M of (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 such that 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 , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-4,
author = {E. Serrano and C. Pi\~neiro and J. M. Delgado},
title = {Some properties and applications of equicompact sets of operators},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {171-180},
zbl = {1127.47022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-4}
}
E. Serrano; C. Piñeiro; J. M. Delgado. Some properties and applications of equicompact sets of operators. Studia Mathematica, Tome 178 (2007) pp. 171-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-4/