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

  • JULIO BECERRA GUERRERO (a1), GINÉS LÓPEZ PÉREZ (a2) and A. RODRÍGUEZ-PALACIOS (a3)

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 $(B_A,{\rm weak)\,{\longrightarrow}\,(B_A,{\rm norm})$.

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

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

  • JULIO BECERRA GUERRERO (a1), GINÉS LÓPEZ PÉREZ (a2) and A. RODRÍGUEZ-PALACIOS (a3)

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