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

Title:

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

Creator:

Krulišová, Hana

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a4543427-0646-4552-a4fe-05b162587ebd
uuid:a4543427-0646-4552-a4fe-05b162587ebd
issn:0011-4642

Subject:

matematika, mathematics, Pełczyński's property (V), $C^*$-algebra, Grothendieck property, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

A Banach space $X$ has Pełczyński's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ 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., Hana Krulišová., and Obsahuje bibliografii

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

937-951

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:4

Harvested from:

CDK

Metadata only:

false