Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T15:39:46.378Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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