Marek CĂșth
Noncommutative Valdivia compacta

Comment.Math.Univ.Carolin. 55,1 (2014) 53-72.

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.

Keywords: retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces
AMS Subject Classification: 46B26 54D30

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