σ -Approximately module amenable Banach algebras

In this paper, we define the notion of sigma-approximate module amenability of Banach algebras and give some properties about this notion. Also for Banach A -bimodule A , and J , the closed ideal of A generated by elements of form ( α · a ) b - a ( b · α ) , ( a , b ∈ A , α ∈ A ) , we considered some corollaries about σ ^ -approximate amenability of A J as a Banach A -bimodule, where σ ^ : A J → A J by σ ^ ( a + J ) = σ ( a ) + J has a dense range.