Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T15:14:37.356Z Has data issue: false hasContentIssue false
  • English
  • Français

CHARACTER AMENABILITY AND CONTRACTIBILITY OF ABSTRACT SEGAL ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  04 August 2010

MAHMOOD ALAGHMANDAN ,
RASOUL NASR-ISFAHANI  and
MEHDI NEMATI
MAHMOOD ALAGHMANDAN
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: m.alaghmandan@math.iut.ac.ir)
RASOUL NASR-ISFAHANI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: isfahani@cc.iut.ac.ir)
MEHDI NEMATI
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: m.nemati@math.iut.ac.ir)
*
✉For correspondence; e-mail: isfahani@cc.iut.ac.ir
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ℬ be an abstract Segal algebra with respect to 𝒜. For a nonzero character ϕ on 𝒜, we study ϕ-amenability, and ϕ-contractibility of 𝒜 and ℬ. We then apply these results to abstract Segal algebras related to locally compact groups.

Keywords

character amenableabstract Segal algebra

MSC classification

Secondary: 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 2 , October 2010 , pp. 274 - 281
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Eymard, P., ‘L’algèbre de Fourier d’un groupe localement compact’, Bull. Soc. Math. France 92 (1964), 181–236.CrossRefGoogle Scholar
[2]Hewitt, E. and Ross, K., Abstract Harmonic Analysis I, Die Grundlehren der Mathematischen Wissenschaften, 115 (Springer-Verlag, Berlin, 1963).Google Scholar
[3]Hewitt, E. and Ross, K., Abstract Harmonic Analysis II, Die Grundlehren der Mathematischen Wissenschaften, 152 (Springer-Verlag, New York, 1970).Google Scholar
[4]Hu, Z., Monfared, M. S. and Traynor, T., ‘On character amenable Banach algebras’, Studia Math. 193 (2009), 53–78.CrossRefGoogle Scholar
[5]Johnson, B. E., ‘Weak amenability of group algebras’, Bull. London Math. Soc. 23 (1991), 281–284.CrossRefGoogle Scholar
[6]Kaniuth, E., A Course in Commutative Banach Algebras (Springer, New York, 2009).CrossRefGoogle Scholar
[7]Kaniuth, E., Lau, A. T. and Pym, J., ‘On ϕ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96.CrossRefGoogle Scholar
[8]Kaniuth, E., Lau, A. T. and Pym, J., ‘On character amenability of Banach algebras’, J. Math. Anal. Appl. 344 (2008), 942–955.CrossRefGoogle Scholar
[9]Monfared, M. S., ‘Character amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 697–706.CrossRefGoogle Scholar
[10]Reiter, H., L 1-algebras and Segal Algebras, Lecture Notes in Mathematics, 231 (Springer, Berlin, 1971).CrossRefGoogle Scholar
[11]Reiter, H. and Stegeman, J. D., Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press, Oxford, 2000).CrossRefGoogle Scholar
[12]Runde, V., Lectures on Amenability (Springer, New York, 2002).CrossRefGoogle Scholar
[13]Samea, H., ‘Essential amenability of abstract Segal algebras’, Bull. Aust. Math. Soc. 79 (2009), 319–325.CrossRefGoogle Scholar
[14]Tewari, U. B. and Parthasarathy, K., ‘A theorem on abstract Segal algebras over some commutative Banach algebras’, Bull. Aust. Math. Soc. 25 (1982), 293–301.CrossRefGoogle Scholar