Banach Journal of Mathematical Analysis

Banach--Saks properties of $C^*$-algebras and Hilbert $C^*$-modules

Michael Frank and Alexander A. Pavlov

Full-text: Open access

Abstract

The investigation of $C^*$-algebras and Hilbert $C^*$-modules with respect to the classical, the weak and the uniform weak Banach--Saks properties is completed giving a full picture, in particular in the non-unital cases. This way some open questions by M. Kusuda and C.-H. Chu are answered. Criteria and structural characterizations are given. In particular, the weak and the uniform weak Banach--Saks property turn out to be invariant under strong Morita equivalence for non-unital $C^*$-algebras.

Article information

Source
Banach J. Math. Anal., Volume 3, Number 2 (2009), 91-102.

Dates
First available in Project Euclid: 17 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1261086713

Digital Object Identifier
doi:10.15352/bjma/1261086713

Mathematical Reviews number (MathSciNet)
MR2545176

Zentralblatt MATH identifier
1206.46009

Subjects
Primary: 46B07: Local theory of Banach spaces
Secondary: 46L08: $C^*$-modules 46L05: General theory of $C^*$-algebras

Keywords
Banach--Saks properties $C^*$-algebras Hilbert $C^*$-modules Morita equivalence

Citation

Frank, Michael; Pavlov, Alexander A. Banach--Saks properties of $C^*$-algebras and Hilbert $C^*$-modules. Banach J. Math. Anal. 3 (2009), no. 2, 91--102. doi:10.15352/bjma/1261086713. https://projecteuclid.org/euclid.bjma/1261086713


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