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 $\phi.$
Citation
M. Essmaili. M. Fozouni. J. Laali. "Hereditary properties of character injectivity with applications to semigroup algebras." Ann. Funct. Anal. 6 (2) 162 - 172, 2015. https://doi.org/10.15352/afa/06-2-14
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