# Connes amenability for certain product of Banach algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan, Iran

2 Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.O. Box 44891-63157, Rudsar, Iran

10.22072/wala.2021.135909.1301

Abstract

In this paper we develop the notions of Connes amenability for certain product of Banach algebras. We give necessary and sufficient conditions for the existence of an invariant mean on the predual of $\Theta$-Lau product  $\mathcal{A}\times_{\Theta}\mathcal{B}$, module extension Banach algebra $\mathcal{A}\oplus\mathcal{X}$ and projective tensor product $\mathcal{A} \widehat{{\otimes}} \mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are dual Banach algebras  with preduals $\mathcal{A}_*$ and $\mathcal{B}_*$ respectively and $\mathcal{X}$ is a normal Banach $\mathcal{A}$-bimodule with predual $\mathcal{X}_*$.

Keywords

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