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arXiv · 1605.04900

C*-algebras have a quantitative version of Pelczynski's property (V)

Hana Krulisova
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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.

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Hana Krulisova. 2016-06-06. C*-algebras have a quantitative version of Pelczynski's property (V). https://arxiv.org/abs/1605.04900

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