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