Hereditary properties of character injectivity with applications to semigroup algebras

Abstract

In this paper, we investigate the notion $\varphi$-injectivity for Banach $A$-modules, where $\varphi$ is a character on $A.$ We obtain some hereditary properties of $\varphi$-injectivity for certain classes of Banach modules related to closed ideals. These results allow us to study $\varphi$-injectivity of certain Banach $A$-modules in commutative case, specially ${\ell }^1$-semilattice algebras. As an application, we give an example of a non-injective Banach module which is $\varphi$-injective for each character $\varphi .$

10 pages, To appear in "Annals of Functional Analysis"

Cited by in corpus (1)

• Primitive orthogonal idempotents of Brandt semigroup algebras