Let A be a left ϕ-amenable Banach algebra, where ϕ denotes a nonzero character on A. In
this paper, we show that the existence of a nonzero compact or weakly compact right …

Let A be a Banach algebra and let ϕ be a nonzero character on A. For a locally compact
group G, let the group algebra L 1 (G) be a closed two-sided ideal in A. In this paper, we aim …

In this paper, we investigate the notion $\phi $-injectivity for Banach $ A $-modules, where
$\phi $ is a character on $ A. $ We obtain some hereditary properties of $\phi $-injectivity for …

Let AA be a Banach*∗-algebra and let φ φ be a nonzero self-adjoint character on A A. For
a*∗-representation π π of AA on a Hilbert space HH, we introduce and study strong φ φ …

In this paper, we study the notion of $\phi $-injectivity in the special case that $\phi= 0$. For
an arbitrary locally compact group $ G $, we characterize the 0-injectivity of $ L^{1}(G) $ as a …

For a Banach algebra ${\cal A} $, we introduce and investigate weak amenability of ${\cal A}
$ with respect to a character. We give some necessary conditions for the weak amenability …

In this paper, some homological notions of Banach A-modules such as ϕinjectivity, 0-
injectivity and character injectivity are discussed, where ϕ is a non-zero multiplicative linear …

Let $ A $ be a Banach algebra, $\Omega (A) $ be the character space of $ A $ and
$\alpha\in\Omega (A) $. In this paper, we examine the characteristics of $\alpha $-projective …

In this work, we give a brief account of the notion of inner amenability that has been
extensively studied in the last four decades. This terminology was first introduced by Effros in …

We study a finite dimensional invariant subspace property similar to Fan's Theorem on
semigroups for arbitrary Banach algebras A in terms of amenability of X (A, ϕ), the closed …