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arXiv · 1303.5557

Separable $C^{\ast}$-Algebras and weak$^{\ast}$-fixed point property

Gero Fendler·Michael Leinert
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Abstract

It is shown that the dual $\hat{A}$ of a separable $C^{\ast}$-algebra $A$ is discrete if and only if its Banach space dual has the weak$^{\ast}$-fixed point property. We prove further that these properties are equivalent to the uniform weak$^{\ast}$ Kadec-Klee property of $A^{\ast}$ and to the coincidence of the weak$^{\ast}$ topology with the norm topology on the pure states of $A$.

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Gero Fendler, Michael Leinert. 2013-03-22. Separable $C^{\ast}$-Algebras and weak$^{\ast}$-fixed point property. https://arxiv.org/abs/1303.5557

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