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Some homological properties of \({T}\)-Lau product algebras

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Abstract

Let \({T}\) be a homomorphism from a Banach algebra \({B}\) to a Banach algebra \({A}\). The Cartesian product space \({A\times B}\) with \({T}\)-Lau multiplication and \({\ell^1}\)-norm becomes a new Banach algebra \({A\times _T B}\). We investigate the notions such as approximate amenability, pseudo amenability, \({\phi}\)-pseudo amenability, \({\phi}\)-biflatness and \({\phi}\)-biprojectivity for Banach algebra \({A\times_T B}\). We also present an example to show that approximate amenability of \({A}\) and \({B}\) is not stable for \({A\times _TB}\). Finally we characterize the double centralizer algebra of \({A\times _T B}\) and present an application of this characterization.

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  1. Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 15914, Tehran, 424 Hafez Avenue, Iran

    A. Pourabbas & N. Razi

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  1. A. Pourabbas
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  2. N. Razi
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Correspondence to A. Pourabbas.

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Pourabbas, A., Razi, N. Some homological properties of \({T}\)-Lau product algebras. Acta Math. Hungar. 149, 31–49 (2016). https://doi.org/10.1007/s10474-016-0610-5

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  • DOI: https://doi.org/10.1007/s10474-016-0610-5

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