## Annals of Functional Analysis

### Hereditary properties of character injectivity with applications to semigroup algebras

#### 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 $\phi.$

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 2 (2015), 162-172.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1418997774

Digital Object Identifier
doi:10.15352/afa/06-2-14

Mathematical Reviews number (MathSciNet)
MR3292523

Zentralblatt MATH identifier
1329.46046

#### Citation

Essmaili, M.; Fozouni, M.; Laali, J. Hereditary properties of character injectivity with applications to semigroup algebras. Ann. Funct. Anal. 6 (2015), no. 2, 162--172. doi:10.15352/afa/06-2-14. https://projecteuclid.org/euclid.afa/1418997774

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