Abstract
Let A and B be Banach algebras, \(\theta : A\rightarrow B\) be a continuous Banach algebra homomorphism and I be a closed ideal in B. Then the direct sum of A and I with respect to \(\theta \), denoted \(A\bowtie ^{\, \theta }I\), with a special product becomes a Banach algebra which is called the amalgamated Banach algebra. In this paper, among other things, we compute the topological centre of \(A\bowtie ^{\, \theta }I\) in terms of that of A and I. Using this, we provide a characterization of the Arens regularity of \(A\bowtie ^{\, \theta }I\). Then we determine the character space of \(A\bowtie ^{\, \theta }I\) in terms of that of A and I. Moreover, we study the weak amenability of \(A\bowtie ^{\, \theta }I\).
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The first author is supported by University of Tabriz.
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Pourmahmood Aghababa, H., Shirmohammadi, N. On amalgamated Banach algebras. Period Math Hung 75, 1–13 (2017). https://doi.org/10.1007/s10998-016-0159-7
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DOI: https://doi.org/10.1007/s10998-016-0159-7