Ali Ghaffari - Department of Mathematics, University of Semnan, P.O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran
Samaneh Javadi - Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.O. Box ۴۴۸۹۱-۶۳۱۵۷, Rudsar, Iran
Ebrahim Tamimi - Department of Mathematics, University of Semnan, P.O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran

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}_*.

Connes amenability, Banach algebras, derivation, group algebra, invariant mean