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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 33, Fasc. 2,
pages 233 - 241
 

SEPARABLE C * -ALGEBRAS AND WEAK* FIXED POINT PROPERTY

Gero Fendler
Michael Leinert

Abstract: We show that the spectrum ^A of a separable C* -algebra A is discrete if and only if A * , the Banach space dual of A , has the weak* fixed point property. We prove further that these properties are equivalent among others 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 . If one assumes the set-theoretic diamond axiom, then the separability is necessary.

2000 AMS Mathematics Subject Classification: Primary: 46L05, 47L50; Secondary: 46L30, 47H10.

Keywords and phrases: Weak* fixed point property, discrete dual, UKK*.

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