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RELATIVELY WEAKLY OPEN SETS IN CLOSED BALLS OF $C^*$-ALGEBRAS

Published online by Cambridge University Press:  17 November 2003

JULIO BECERRA GUERRERO ,
GINÉS LÓPEZ PÉREZ  and
A. RODRÍGUEZ-PALACIOS
JULIO BECERRA GUERRERO
Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071-Granada, [email protected]
GINÉS LÓPEZ PÉREZ
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, [email protected]
A. RODRÍGUEZ-PALACIOS
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, [email protected]
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Abstract

Let $A$ be an infinite-dimensional $C^*$-algebra. It is proved that every nonempty relatively weakly open subset of the closed unit ball $B_A$ of $A$ has diameter equal to 2. This implies that $B_A$ is not dentable, and that there is not any point of continuity for the identity mapping $(B_A,{\rm weak)\,{\longrightarrow}\,(B_A,{\rm norm})$.

Keywords

46B0446B2246L0546L70 (primary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 753 - 761
Copyright
The London Mathematical Society 2003

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Footnotes

This work was partially supported by Junta de Andalucía grant FQM 0199.