Banach Journal of Mathematical Analysis

Errata on "Banach-Saks properties of C*-algebras and Hilbert C*-modules"

Michael Frank and Alexander A. Pavlov

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Due to an example indicated to us in September 2009 we have to add one more restriction to the suppositions on the imprimitivity bimodules treated in Proposition 4.1, Theorem 5.1, Theorem 6.2 and Proposition 6.3. In the situation when the Banach-Saks property holds for the imprimitivity bimodule we can describe all possible additional examples violating the newly invented supposition. So the classification of Hilbert $C^*$-modules with the Banach-Saks property is complete. Beyond that, there is still an open problem for a certain class of imprimitivity bimodules with the weak or uniform weak Banach-Saks property which might violate the additional condition.

Article information

Banach J. Math. Anal., Volume 5, Number 1 (2011), 94-100.

First available in Project Euclid: 14 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Banach-Saks properties C*-algebra Hilbert C*-module Morita equivalence


Frank, Michael; Pavlov, Alexander A. Errata on "Banach-Saks properties of C*-algebras and Hilbert C*-modules". Banach J. Math. Anal. 5 (2011), no. 1, 94--100. doi:10.15352/bjma/1313362984.

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