Noncommutative Valdivia compacta

Marek Cúth

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 1, page 53-72
  • ISSN: 0010-2628

Abstract

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We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space K , we show that K is Corson if and only if every continuous image of K has a retractional skeleton. We also present some open problems in this area.

How to cite

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Cúth, Marek. "Noncommutative Valdivia compacta." Commentationes Mathematicae Universitatis Carolinae 55.1 (2014): 53-72. <http://eudml.org/doc/260834>.

@article{Cúth2014,
abstract = {We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space $K$, we show that $K$ is Corson if and only if every continuous image of $K$ has a retractional skeleton. We also present some open problems in this area.},
author = {Cúth, Marek},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces; retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces},
language = {eng},
number = {1},
pages = {53-72},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Noncommutative Valdivia compacta},
url = {http://eudml.org/doc/260834},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Cúth, Marek
TI - Noncommutative Valdivia compacta
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 1
SP - 53
EP - 72
AB - We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space $K$, we show that $K$ is Corson if and only if every continuous image of $K$ has a retractional skeleton. We also present some open problems in this area.
LA - eng
KW - retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces; retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces
UR - http://eudml.org/doc/260834
ER -

References

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