Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T08:48:51.980Z Has data issue: false hasContentIssue false
  • English
  • Français

On ϕ-amenability of Banach algebras

Published online by Cambridge University Press:  01 January 2008

EBERHARD KANIUTH ,
ANTHONY T. LAU  and
JOHN PYM
EBERHARD KANIUTH
Affiliation:
Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany. e-mail: [email protected]
ANTHONY T. LAU
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada T6G 2G1. e-mail: [email protected]
JOHN PYM
Affiliation:
Department of Mathematics, University of Sheffield, Sheffield S3 7RH. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Generalizing the notion of left amenability for so-called F-algebras [12], we study the concept of ϕ-amenability of a Banach algebra A, where ϕ is a homomorphism from A to ℂ. We establish several characterizations of ϕ-amenability as well as some hereditary properties. In addition, some illuminating examples are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 85 - 96
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bonsall, F. F. and Duncan, J.. Complete Normed Algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
[2]Bunce, J. W.. Characterizations of amenable and strongly amenable C*-algebras. Pacific J. Math 43 (1972), 563–572.CrossRefGoogle Scholar
[3]Bunce, J. W.. Finite operators and amenable C*-algebras. Proc. Amer. Math. Soc 56 (1976), 145–151.Google Scholar
[4]Dales, H. G.. Banach algebras and automatic continuity. London Mathematical Society Monographs (Clarendon Press, 2000).Google Scholar
[5]Doran, R. S. and Wichmann, J.. Approximate identities and factorization in Banach modules Lecture Notes in Math. 768. (Springer-Verlag, 1979).CrossRefGoogle Scholar
[6]Dunford, N. and Schwartz, J. T.. Linear Operators I (Wiley, 1988).Google Scholar
[7]Eymard, P.. L'algébre de Fourier d'un groupe localement compact. Bull. Soc. Math. Franc 92 (1964), 181–236.CrossRefGoogle Scholar
[8]Forrest, B. E. and Runde, V.. Amenability and weak amenability of the Fourier algebra. Math. Z 250 (2005), 731–744.CrossRefGoogle Scholar
[9]Johnson, B. E.. Cohomology in Banach algebras. Mem. Amer. Math. Soc 127 (Providence, 1972).Google Scholar
[10]Johnson, B. E.. Non-amenability of the Fourier algebra of a compact group. J. London Math. Soc. (2) 50 (1994), 361–374.CrossRefGoogle Scholar
[11]Lau, A. T.. Characterization of amenable Banach algebras. Proc. Amer. Math. Soc 70 (1978), 156–160.Google Scholar
[12]Lau, A. T.. Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups. Fund. Math 118 (1983), 161–175.Google Scholar
[13]Monfared, M. S.. Character amenability of Banach algebras, preprint.Google Scholar
[14]Namioka, I.. Folner's condition for amenable semigroups. Math. Scand 15 (1964), 18–28.CrossRefGoogle Scholar
[15]Nasr-Isfahani, R.. Fixed point characterization of left amenable Lau algebras. Internat. J. Math. Sci. 61–64 (2004), 3333–3338.CrossRefGoogle Scholar
[16]Nasr-Isfahani, R.. Strongly amenable *-representations of Lau *-algebras. Rev. Roumaine Math. Pures Appl 49 (2004), 545–556.Google Scholar
[17]Pier, J-P.. Amenable Banach algebras. Pitman Reserarch Notes in Mathematics 172 (Longman Scientific/Technical, 1988).Google Scholar
[18]Schaefer, H. H.. Topological Vector Spaces (Springer-Verlag, 1971).CrossRefGoogle Scholar