We prove that for every group G and any two sets I, J , the Brandt semigroup algebras l(B(I,G)) and l(B(J,G)) are Morita equivalent with respect to the Morita theory of selfinduced Banach algebras introduced by Grønbæk. As applications, we show that if G is an amenable group, then for a wide class of Banach l(B(I,G))-bimodules E, and every n > 0, the bounded Hochschild cohomology groups H(l(B(I...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...