Abstract of a paper by Gero Fendler and Michael Leinert
This is an announcement for the paper "Separable $C^{\ast}$-algebras and weak$^{\ast}$-fixed point property" by Gero Fendler and Michael Leinert. Abstract: It is shown that the dual $\widehat{A}$ 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 $A$. Archive classification: math.OA Mathematics Subject Classification: Primary: 46L05, 47L50, Secondary: 46L30, 47H10 Remarks: 6 pages Submitted from: gero.fendler@univie.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.5557 or http://arXiv.org/abs/1303.5557
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