Skip to main content
SpringerLink
Log in

Essential character amenability of semigroup algebras

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

Let S be a foundation topological semigroup and \(M_a(S)\) the space of all measures \(\mu \in M(S)\) for which the maps \(x\longmapsto |\mu |*\delta _{x}\) and \(x\longmapsto \delta _{x}*|\mu |\) from S into M(S) are weakly continuous. In the present paper, we introduce and study the concept of \(\phi\)-amenability for S and investigate the relations between \(\phi\)-amenability of S and essential \(\widehat{\phi }\)-amenability of \(M_a(S)\), where \(\phi\) is a character on S and \(\widehat{\phi }\) is the extension of \(\phi\) to \(M_a(S)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baker, A.C., Baker, J.W.: Algebra of measures on a locally compact semigroup III. J. Lond. Math. Soc. 4, 685–695 (1972)

    Article  MathSciNet  Google Scholar 

  2. Bodaghi, A., Jabbari, A., Amini, M.: Character inner amenability for semigroups. Semigroup Forum 100, 439–450 (2020)

    Article  MathSciNet  Google Scholar 

  3. Dales, H.G.: Banach Algebras and Automatic Continuity. Clarendon Press, Oxford (2000)

    MATH  Google Scholar 

  4. Day, M.M.: Amenable semigroups. Illinois J. Math. 1(4), 509–544 (1957)

    Article  MathSciNet  Google Scholar 

  5. Day, M.M.: Means on semigroups and groups. Bull. Am. Math. Soc. 55, 1054–1055 (1949)

    Google Scholar 

  6. Duncan, J., Namioka, I.: Amenability of inverse semigroups and their semigroup algebras. Proc. Roy. Soc. 80, 309–321 (1998)

    MathSciNet  MATH  Google Scholar 

  7. Dzinotyiweyi, H.A.M.: The Analog of the Group Algebra for Topological Semigroups. Research Notes in Mathematics, vol. 98, Pitman, New York (1984)

  8. Essmaili, M., Filali, M.: \(\phi\)-Amenability and character amenability of some classes of Banach algebras. Houston J. Math. 39, 515–529 (2013)

    MathSciNet  MATH  Google Scholar 

  9. Ghaffari, A.: On character amenability of semigroup algebras. Acta. Math. Hungar. 134, 177–192 (2012)

    Article  MathSciNet  Google Scholar 

  10. Ghahramani, F., Loy, R.J.: Generalized notations of amenability. J. Funct. Anal. Soc. 208, 229–260 (2004)

    Article  Google Scholar 

  11. Johnson, B.E.: Cohomology in Banach algebras. Memoirs Amer. Math. Soc. 127, 96 (1972)

  12. Kaniuth, E., Lau, A., Pym, J.: On \(\varphi\)-amenability of Banach algebras. Math. Proc. Camp. Phil. Soc. 144, 85–96 (2008)

    Article  MathSciNet  Google Scholar 

  13. Kaniuth, E., Lau, A., Pym, J.: On character amenability of Banach algebras. J. Math. Anal. Appl. 344, 942–955 (2008)

    Article  MathSciNet  Google Scholar 

  14. Lashkarizadeh Bami, M.: Ideals of \(M(S)\) as ideals of \({\text{ LUC }}{\mathit{(S)}}^{*}\) of a compactly cancellative semigroup \(S\). Math. Jpn. 48, 363–366 (1998)

    MATH  Google Scholar 

  15. Lashkarizadeh Bami, M.: Representations of foundation semigroups and their algebras. Can. J. Math. 37, 29–47 (1985)

    Article  MathSciNet  Google Scholar 

  16. Lashkarizadeh Bami, M., Mohammadzadeh, B., Samea, H.: Derivations on certain semigroup algebras. J. Sci. I. R. I(18), 339–345 (2007)

    MathSciNet  Google Scholar 

  17. Lashkarizadeh Bami, M., Samea, H.: Approximate amenability of certain semigroup algebras. Semigroup Forum 71, 312–322 (2005)

    Article  MathSciNet  Google Scholar 

  18. Lau, A.T.M.: Amenability of semigroups. In: Hofmann, K.H., Lawson, J.D., Pym, J.S. (eds.) The Analytical and Topological Theory of Semigroups, pp. 313–334. Trends and Developments, Walter de Gruyter, Berlin (1990)

    Google Scholar 

  19. Lau, A.T.M.: Analysis on a class of Banach algebras with application to harmonic analysis on locally compact groups and semigroups. Fund. Math. 118, 161–175 (1983)

    Article  MathSciNet  Google Scholar 

  20. Maepa, S.M., Mewomo, O.T.: On character amenability of semigroup algebras. Quaes. Math. 39, 307–318 (2016)

    Article  MathSciNet  Google Scholar 

  21. Maysami Sadr, M., Pourabbas, A.: Johnson amenability for topological semigroups. Iran J. Sci. Technol. A. 32, 151–160 (2010)

    MathSciNet  Google Scholar 

  22. Monfared, M.S.: Character amenability of Banach algebras. Math. Proc. Camb. Phil. Soc. 144, 697–706 (2008)

    Article  MathSciNet  Google Scholar 

  23. Munn, W.D.: A class of irreducible matrix representations of an arbitrary inverse semigroup. Proc. Glasgow Math. Assoc. 5, 41–48 (1961)

    Article  MathSciNet  Google Scholar 

  24. Namioka, I.: On certain actions of semigroups on L-spaces. Studia Math. 29, 63–77 (1967)

    Article  MathSciNet  Google Scholar 

  25. Nasr-Isfahani, R., Nemati, M.: Essential character amenability of Banach algebras. Bull. Aust. Math. Soc. 84, 372–386 (2011)

    Article  MathSciNet  Google Scholar 

  26. Runde, V.: Lectures on Amenability. Lecture Notes in Mathematics, vol. 1774. Springer-Verlag, Berlin-Heidelberg-New York (2002)

  27. Sadeghi Nahrekhalaji, H.: Essential character contractibility of Banach algebras. U. P. B. Sci. Bull., Ser. A 81(2), 165–176 (2019)

    MathSciNet  Google Scholar 

  28. von Neumann, J.: Almost periodic functions in a group I. Trans. Am. Math. Soc. 36(3), 445–492 (1934)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Young Researchers and Elite Club, Fereydan Branch, Islamic Azad University, Isfahan, Iran

    Hamid Sadeghi Nahrekhalaji

Authors
  1. Hamid Sadeghi Nahrekhalaji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamid Sadeghi Nahrekhalaji.

Additional information

Communicated by Anthony To-Ming Lau.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nahrekhalaji, H.S. Essential character amenability of semigroup algebras. Semigroup Forum 102, 528–542 (2021). https://doi.org/10.1007/s00233-020-10155-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-020-10155-w

Keywords

Search

Navigation