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A NOTE ON CYCLIC AMENABILITY OF THE LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM
Published online by Cambridge University Press: 16 June 2015
Abstract
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
MSC classification
- 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.
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