In this paper, for the Banach algebra AT , we study the various notions of amenability like pseudo amenability, Johnson pseudo-contractibility and module amenability, where A is a Banach algebra and T is a left multiplier on A. For a dual Banach algebra A, under some conditions, we show that if AT is Connes amenable (resp. Connes biprojective), then A is Connes amenable (resp. Connes biprojective). For a non-zero multiplicative linear functional ’ : A ! C, we study the relationship between ’-amenability of A and ’R-amenability of AT , where (T; R) be a double centralizer of A.
