Bulletin of the Belgian Mathematical Society - Simon Stevin

Approximate injectivity of dual Banach algebras

Amin Mahmoodi

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Abstract

A new notion of injectivity is introduced. It is shown that approximate Connes-amenability and approximate injectivity are the same properties. As a consequence, approximate Connes-amenability of the direct sum of dual Banach algebras is discussed. A characterization is given for approximate Connes-amenability of dual Banach algebras in terms of the approximate splitting of certain short exact sequence.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 5 (2013), 831-842.

Dates
First available in Project Euclid: 25 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1385390767

Digital Object Identifier
doi:10.36045/bbms/1385390767

Mathematical Reviews number (MathSciNet)
MR3160592

Zentralblatt MATH identifier
1285.22011

Subjects
Primary: 22D15: Group algebras of locally compact groups 43A10: Measure algebras on groups, semigroups, etc.
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc. 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Keywords
Connes-amenable dual Banach algebras Approximately Connes-amenable dual Banach algebras Approximately injective dual Banach algebras

Citation

Mahmoodi, Amin. Approximate injectivity of dual Banach algebras. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 831--842. doi:10.36045/bbms/1385390767. https://projecteuclid.org/euclid.bbms/1385390767


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