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

Gero Fendler; Michael Leinert

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

Operator Algebras 2013-06-14 v2

Authors: Gero Fendler , Michael Leinert

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 $A$ .

Keywords

banach space properties banach algebras c*-algebras

Cite

@article{arxiv.1303.5557,
  title  = {Separable $C^{\ast}$-Algebras and weak$^{\ast}$-fixed point property},
  author = {Gero Fendler and Michael Leinert},
  journal= {arXiv preprint arXiv:1303.5557},
  year   = {2013}
}

Comments

a proof revised, some results and references added, 7 pages

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