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

Hana Krulišová

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 937-951
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Krulišová, Hana. "C*-algebras have a quantitative version of Pełczyński's property (V)." Czechoslovak Mathematical Journal 67.4 (2017): 937-951. <http://eudml.org/doc/294226>.

@article{Krulišová2017,
abstract = {A Banach space $X$ has Pełczyński’s property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\rightarrow Y$ 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.},
author = {Krulišová, Hana},
journal = {Czechoslovak Mathematical Journal},
keywords = {Pełczyński’s property (V); $C^*$-algebra; Grothendieck property},
language = {eng},
number = {4},
pages = {937-951},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {C*-algebras have a quantitative version of Pełczyński's property (V)},
url = {http://eudml.org/doc/294226},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Krulišová, Hana
TI - C*-algebras have a quantitative version of Pełczyński's property (V)
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 937
EP - 951
AB - A Banach space $X$ has Pełczyński’s property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\rightarrow Y$ 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.
LA - eng
KW - Pełczyński’s property (V); $C^*$-algebra; Grothendieck property
UR - http://eudml.org/doc/294226
ER -

References

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