Abstract
A Banach space X has Pełczyński’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 Pełczyński’s property (V). In the preprint (Krulišová, (2015)) 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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The research was supported by Grant No. 142213/B-MAT/MFF of the Grant Agency of the Charles University in Prague and by Research grant GA ČR P201/12/0290.
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Krulišová, H. C*-algebras have a quantitative version of Pełczyński’s property (V). Czech Math J 67, 937–951 (2017). https://doi.org/10.21136/CMJ.2017.0242-16
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DOI: https://doi.org/10.21136/CMJ.2017.0242-16