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arXiv · 1501.00535

Hereditary properties of character injectivity with applications to semigroup algebras

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 $\phi.$

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M. Essmaili, M. Fozouni, J. Laali. 2015-01-03. Hereditary properties of character injectivity with applications to semigroup algebras. https://doi.org/10.15352/afa/06-2-14

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