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 $\phi.$
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1501.00535
- arXiv:
- arXiv:1501.00535
- Bibcode:
- 2015arXiv150100535E
- Keywords:
-
- Mathematics - Functional Analysis;
- 46M10;
- 43A20;
- 46H25
- E-Print:
- 10 pages, To appear in "Annals of Functional Analysis"