Hereditary properties of character injectivity with applications to semigroup algebras

M. Essmaili; M. Fozouni; J. Laali

doi:10.15352/afa/06-2-14

Hereditary properties of character injectivity with applications to semigroup algebras

Functional Analysis 2016-03-10 v1

Authors: M. Essmaili , M. Fozouni , J. Laali

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Abstract

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 certain classes of Banach modules related to closed ideals. These results allow us to study $\phi$ -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 $\phi$ -injective for each character $\phi.$

Keywords

phi-injectivity banach modules character hereditary properties closed ideals semigroup algebras semilattice algebras

Cite

@article{arxiv.1501.00535,
  title  = {Hereditary properties of character injectivity with applications to semigroup algebras},
  author = {M. Essmaili and M. Fozouni and J. Laali},
  journal= {arXiv preprint arXiv:1501.00535},
  year   = {2016}
}

Comments

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

Hereditary properties of character injectivity with applications to semigroup algebras

Abstract

Keywords

Cite

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