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ON $\varphi $-AMENABILITY OF DUAL BANACH ALGEBRAS

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

Published online by Cambridge University Press:  09 July 2021

ALIREZA JABERI Open the ORCID record for ALIREZA JABERI [Opens in a new window]  and
AMIN MAHMOODI Open the ORCID record for AMIN MAHMOODI [Opens in a new window]
ALIREZA JABERI
Affiliation:
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran e-mail: [email protected]
AMIN MAHMOODI*
Affiliation:
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
*
e-mail: [email protected]
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Abstract

Generalising the concept of injectivity, we study the notion of $\varphi $ -injectivity for dual Banach algebras. It provides a framework for studying $\varphi $ -amenability of enveloping dual Banach algebras.

Keywords

φ-amenabilityφ-injectivitydual Banach algebras

MSC classification

Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 2 , April 2022 , pp. 303 - 313
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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References

Daws, M., ‘Dual Banach algebras: representations and injectivity’, Studia Math. 178 (2007), 231–275.10.4064/sm178-3-3CrossRefGoogle Scholar
Hu, Z., Monfared, M. S. and Traynor, T., ‘On character amenable Banach algebras’, Studia Math. 193 (2009), 53–78.10.4064/sm193-1-3CrossRefGoogle Scholar
Johnson, B. E., Cohomology in Banach Algebras , Memoirs of the American Mathematical Society, 127 (American Mathematical Society, Providence, RI, 1972).10.1090/memo/0127CrossRefGoogle Scholar
Kaniuth, E., Lau, A. T. and Pym, J., ‘On $\varphi$ -amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96.10.1017/S0305004107000874CrossRefGoogle Scholar
Lau, A. T., ‘Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups’, Fund. Math. 118 (1983), 161–175.Google Scholar
Mahmoodi, A., ‘On $\varphi$ -Connes amenability of dual Banach algebras’, J. Linear Topol. Algebra 3 (2014), 211–217.Google Scholar
Mahmoodi, A., ‘ $\varphi$ -contractibility and $\varphi$ -Connes amenability coincide with some older notions’, Bull. Aust. Math. Soc. 97 (2018), 274–278.CrossRefGoogle Scholar
Monfared, M. S., ‘Character amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 697–706.10.1017/S0305004108001126CrossRefGoogle Scholar
Runde, V., ‘Amenability for dual Banach algebras’, Studia Math. 148 (2001), 47–66.10.4064/sm148-1-5CrossRefGoogle Scholar
Runde, V., ‘Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule’, Math. Scand. 95 (2004), 124–144.10.7146/math.scand.a-14452CrossRefGoogle Scholar
Runde, V., Amenable Banach Algebras: A Panorama , Springer Monographs in Mathematics (Springer, New York, 2020).10.1007/978-1-0716-0351-2CrossRefGoogle Scholar