Separable C^∗-Algebras and weak^∗-fixed point property

2013/03/22 by Gero Fendler, Fendler, Gero, Michael Leinert +1
Mathematics · #47H10 #47L50 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Combinatorics #Discrete mathematics #Epistemology #FOS: Mathematics #Fixed point #Fixed-point property #Fixed-point theorem #Geometry #Mathematical analysis #Mathematics #Operator Algebras (math.OA) #Philosophy #Point (geometry) #Primary: 46L05 #Property (philosophy) #Pure mathematics #Secondary: 46L30 #Separable space #math.OA #msc:46L05 #msc:46L30 #msc:47H10 #msc:47L50

paper · pdf · doi:10.48550/arxiv.1303.5557

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

openalex publication_date 2013/03/22 · arxiv created 2013/06/13 · arxiv updated 2013/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

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• The fixed point property via dual space properties
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• X^* with weak* uniform Kadec-Klee property has Property(K^*)