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

2016/05/16 by Krulisova, Hana · 1 citation
#46B04 #46L05 #47B10 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1605.04900

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.

Cited by

• Quantitative Schur property and measures of weak non-compactness

Related

• Quantification of Pełczyński's property (V)
• Pelczynski's property (V) on spaces of vector valued functions
• Compact range property and operators on C^*-algebras
• The Pelczynski property for tight subspaces
• 1-Grothendieck C(K) spaces