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A COUNTEREXAMPLE TO A RESULT OF JABERI AND MAHMOODI

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

Published online by Cambridge University Press:  10 August 2023

A. SAHAMI Open the ORCID record for A. SAHAMI [Opens in a new window]  and
S. F. SHARIATI Open the ORCID record for S. F. SHARIATI [Opens in a new window]
A. SAHAMI*
Affiliation:
Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516 Ilam, Iran
S. F. SHARIATI
Affiliation:
Department of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran e-mail: f.shariati@aut.ac.ir
*
e-mail: a.sahami@ilam.ac.ir
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Abstract

We show that $\ell ^1(\mathbb {N}_\wedge )$ is $\varphi $-amenable for each multiplicative linear functional $\varphi :\ell ^1(\mathbb {N}_\wedge )\rightarrow \mathbb {C}.$ This is a counterexample to the final corollary of Jaberi and Mahmoodi [‘On $\varphi $-amenability of dual Banach algebras’, Bull. Aust. Math. Soc. 105 (2022), 303–313] and shows that the final theorem in that paper is not valid.

Keywords

φ-amenabilityBanach algebra

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

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 1 , August 2024 , pp. 155 - 157
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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