C*-algebras have a quantitative version of Pelczynski's property (V)
Abstract
A Banach space X has Pelczynski's property (V) if for every Banach space Y every unconditionally converging operator T: X -> Y is weakly compact. H. Pfitzner proved that C*-algebras have Pelczynski's property (V). In the preprint "H. Krulisova: Quantification of Pelczynski's property (V)" the author explores possible quantifications of the property (V) and shows that C(K) spaces for a compact Hausdorff space K enjoy a quantitative version of the property (V). In this paper we generalize this result by quantifying Pfitzner's theorem. Moreover, we prove that in dual Banach spaces a quantitative version of the property (V) implies a quantitative version of the Grothendieck property.
Keywords
Cite
@article{arxiv.1605.04900,
title = {C*-algebras have a quantitative version of Pelczynski's property (V)},
author = {Hana Krulisova},
journal= {arXiv preprint arXiv:1605.04900},
year = {2016}
}
Comments
12 pages, some minor mistakes have been corrected, one theorem has been improved and its proof simplified