Annals of Functional Analysis

Hereditary properties of character injectivity with applications to semigroup algebras

M. Essmaili, M. Fozouni, and 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 $\phi.$

Article information

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

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
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

Subjects
Primary: 46M10: Projective and injective objects [See also 46A22]
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc. 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Keywords
Injectivity $\phi$-injectivity $\phi$-amenability semigroup algebras

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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References

  • H.G. Dales, Banach algebras and automatic continuity, Clarendon press, Oxford, 2000.
  • H.G. Dales, A.T. Lau and D. Strauss, Banach algebras on semigroups and their compactifications, Mem. Amer. Math. Soc. 205 (2010), no. 966, 165 pp.
  • H.G. Dales and M.E. Polyakov, Homological properties of modules over group algebras, Proc. London Math. Soc. 89 (2004), 390–426.
  • M. Essmaili and M. Filali, $\phi$-amenability and character amenability of some classes of Banach algebras, Houston J. Math. 39. no. 2 (2013), 515–529.
  • B.E. Forrest, Amenability and bounded approximate identities in ideals of $A(G)$, Illinois J. Math. 34. no. 1 (1990), 1–25.
  • A.Ya. Helemskii, A certain class of flat Banach modules and its applications, Vestnik. Moskov. Univ. Ser. Mat. Mekh. 27 (1972), 29–36.
  • E. Kaniuth, A.T. Lau and J.S. Pym, On $\varphi$-amenability of Banach algebras, Math. Proc. Cambridge philos. Soc. 144 (2008), 85–96.
  • E. Kaniuth, A.T. Lau and J.S. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl. 344 (2008), 942–955.
  • M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008), 697–706.
  • R. Nasr-Isfahani and S. Soltani Renani, Character injectivity and projectivity of Banach modules, Quart. J. Math. 65 (2) (2014), 665–676.
  • P. Ramsden, Homological properties of modules over semigroup algebras, J. Funct. Anal. 258 (2010) 3988–4009.
  • P. Ramsden, Homological properties of semigroup algebras, Ph. D. Thesis, University of Leeds, 2008.
  • M. C. White, Injective modules for uniform algebras, Proc. London Math. Soc. (3) 73 (1996), 155–184.