We give sufficient conditions for subsets of compact operators to be weakly precompact. Let (resp. ) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F. We prove that if H is a subset of such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results: If E has property (wV*) and F has property (V*), then has property (wV*). Suppose that . Then has property (V*) if and only if E and F have property (V*).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-10,
author = {Ioana Ghenciu},
title = {Weak precompactness and property (V*) in spaces of compact operators},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {255-269},
zbl = {1330.46023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-10}
}
Ioana Ghenciu. Weak precompactness and property (V*) in spaces of compact operators. Colloquium Mathematicae, Tome 139 (2015) pp. 255-269. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-10/