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$\unicode[STIX]{x1D711}$-CONTRACTIBILITY AND $\unicode[STIX]{x1D711}$-CONNES AMENABILITY COINCIDE WITH SOME OLDER NOTIONS

Part of: Topological algebras, normed rings and algebras, Banach algebras Homological methods Abstract harmonic analysis

Published online by Cambridge University Press:  30 January 2018

AMIN MAHMOODI Open the ORCID record for AMIN MAHMOODI [Opens in a new window]
AMIN MAHMOODI*
Affiliation:
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran email a_mahmoodi@iauctb.ac.ir
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Abstract

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It is shown that various definitions of $\unicode[STIX]{x1D711}$-Connes amenability and $\unicode[STIX]{x1D711}$-contractibility are equivalent to older and simpler concepts.

Keywords

𝜑-amenability𝜑-contractibility𝜑-Connes amenability

MSC classification

Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 274 - 278
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Chevreau, B., Jung, I. B., Ko, E. and Pearcy, C., ‘Weak∗ continuous characters on dual algebras’, Indiana Univ. Math. J. 54 (2005), 187–198.Google Scholar
Ghaffari, A. and Javadi, S., ‘𝜑-Connes amenability of dual Banach algebras’, Bull. Iranian Math. Soc. 43 (2017), 25–39.Google Scholar
Helemskii, A. Ya., The Homology of Banach and Topological Algebras (Springer, Netherlands, 1989) (translated from the Russian).Google Scholar
Hu, Z., Monfared, M. S. and Traynor, T., ‘On character amenable Banach algebras’, Studia Math. 193(1) (2009), 53–78.Google Scholar
Johnson, B. E., Cohomology in Banach Algebras, Memoirs of American Mathematical Society, 127 (American Mathematical Society, Providence, RI, 1972).Google Scholar
Kaniuth, E., Lau, A. T. and Pym, J., ‘On 𝜑-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96.Google Scholar
Mahmoodi, A., ‘On 𝜑-Connes amenability of dual Banach algebras’, J. Linear Topol. Algebra 3 (2014), 211–217.Google Scholar
Monfared, M. S., ‘Character amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 697–706.Google Scholar
Runde, V., ‘Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule’, Math. Scand. 95 (2004), 124–144.Google Scholar
Shojaee, B. and Amini, M., ‘Character Connes-amenability of dual Banach algebras’, Period. Math. Hungar. 74 (2017), 31–39.Google Scholar
White, M. C., ‘Injective modules for uniform algebras’, Proc. Lond. Math. Soc. 73(1) (1996), 155–184.Google Scholar