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A NOTE ON CYCLIC AMENABILITY OF THE LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  16 June 2015

F. ABTAHI  and
A. GHAFARPANAH
F. ABTAHI*
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email abtahi.fatemeh@yahoo.com, f.abtahi@sci.ui.ac.ir
A. GHAFARPANAH
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email ghafarpanah@sci.ui.ac.ir, ghafarpanah2002@gmail.com
*
✉abtahi.fatemeh@yahoo.com
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Abstract

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Let $T$ be a Banach algebra homomorphism from a Banach algebra ${\mathcal{B}}$ to a Banach algebra ${\mathcal{A}}$ with $\Vert T\Vert \leq 1$. Recently, Bhatt and Dabhi [‘Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism’, Bull. Aust. Math. Soc.87 (2013), 195–206] showed that cyclic amenability of ${\mathcal{A}}\times _{T}{\mathcal{B}}$ is stable with respect to $T$, for the case where ${\mathcal{A}}$ is commutative. In this note, we address a gap in the proof of this stability result and extend it to an arbitrary Banach algebra ${\mathcal{A}}$.

Keywords

cyclic amenabilityT-Lau product

MSC classification

Primary: 46H05: General theory of topological algebras
Secondary: 46H99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 282 - 289
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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Bhatt, S. J. and Dabhi, P. A., ‘Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism’, Bull. Aust. Math. Soc. 87 (2013), 195–206.CrossRefGoogle Scholar
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