Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T14:30:50.104Z Has data issue: false hasContentIssue false
  • English
  • Français

The ideal structure of some Banach algebras

Published online by Cambridge University Press:  24 October 2008

M. Filali
M. Filali
Affiliation:
Department of Mathematics, University of Oulu, 90570, Finland
Get access Rights & Permissions [Opens in a new window]

Abstract

Let G be a locally compact group and let Ĝ be its character group. Among other results, the minimal left ideals of L∞(G)* and LUC(G)* are all found when G is abelian. The main tool used for this study is the set of (topological) χ-invariant functionals (χ∈Ĝ), defined in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 567 - 576
Copyright
Copyright © Cambridge Philosophical Society 1992

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]Arens, R.. Operations induced in function classes. Monatsh. Math. 55 (1951), 1–19.CrossRefGoogle Scholar
[2]Baker, J. W. and Butcher, R. J.. The Stone–Čech compactification of a topological semigroup. Math. Proc. Cambridge Philos. Soc. 80 (1976), 103–107.CrossRefGoogle Scholar
[3]Baker, J. W. and Milnes, P.. The ideal structure of the Stone–Čech compactification of a group. Math. Proc. Cambridge Philos. Soc. 82 (1977), 401–409.CrossRefGoogle Scholar
[4]Berglund, J. F., Junghenn, H. D. and Milnes, P.. Compact Right Topological Semigroups and Generalisations of Almost Periodicity. Lecture Notes in Math. vol. 663 (Springer-Verlag, 1978).CrossRefGoogle Scholar
[5]Berglund, J. F.., Junghenn, H. D. and Milnes, P.. Analysis on Semigroups: Function Spaces, Compactifications, Representations (Wiley, 1989).Google Scholar
[6]Chou, C.. On topologically invariant means on a locally compact group. Trans. Amer. Math. Soc. 151 (1970), 443–456.CrossRefGoogle Scholar
[7]Civin, P.. Ideals in the second conjugate algebra of a group algebra. Math. Scand. 11 (1962), 161–174.CrossRefGoogle Scholar
[8]Civin, P. and Yood, B.. The second conjugate space of a Banach algebra as an algebra. Pacific J. Math. 11 (1961), 847–870.CrossRefGoogle Scholar
[9]Duncan, J. and Hosseiniun, S. A. R.. The second dual of a Banach algebra. Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 309–325.CrossRefGoogle Scholar
[10]Filali, M.. The uniform compactification of a locally compact abelian group. Math. Proc. Cambridge Philos. Soc. 108 (1990), 527–538.CrossRefGoogle Scholar
[11]Granirer, E. E.. The radical of L ∞(G)*. Proc. Amer. Math. Soc. 41 (1973), 321–324.Google Scholar
[12]Greenleaf, F. P.. Invariant Means on Topological Groups and their Applications (Van Nostrand, 1969).Google Scholar
[13]Grosser, M. and Losert, V.. The norm-strict bidual of a Banach algebra and the dual of Cu(G). Manuscripta Math. 45 (1984), 127–146.CrossRefGoogle Scholar
[14]Gulick, S. L.. Commutativity and ideals in the biduals of topological algebras. Pacific J. Math. 18 (1966), 121–137.CrossRefGoogle Scholar
[15]Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis, vol. 1 (Springer-Verlag, 1963).Google Scholar
[16]Lau, A. T. M.. Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semi-groups. Math. Proc. Cambridge Philos. Soc. 99 (1986), 273–283.CrossRefGoogle Scholar
[17]Lau, A. T. M. and Losert, V.. On the second conjugate algebra of L 1(G) of a locally compact group. J. London Math. Soc. (2) 37 (1988), 464–470.CrossRefGoogle Scholar
[18]Loomis, L. H.. An Introduction to Abstract Harmonic Analysis (Van Nostrand, 1953).Google Scholar
[19]Naimark, M. A.. Normed Algebras (Wolters-Noordhoff, 1972).Google Scholar
[20]Olubummo, A.. Finitely additive measures on the non-negative integers. Math. Scand. 24 (1969), 186–194.CrossRefGoogle Scholar
[21]Paterson, A. L. T.. Amenability (American Mathematical Society, 1988).CrossRefGoogle Scholar
[22]Rickart, C. E.. General Theory of Banach Algebras (Van Nostrand, 1960).Google Scholar
[23]Silbermann, B.. Analysis on Toeplitz Operators (Akademie-Verlag, 1989; Springer-Verlag, 1989).Google Scholar
[24]Wong, J. C. S.. Topologically stationary locally compact groups and amenability. Trans. Amer. Math. Soc. 114 (1969), 351–363.CrossRefGoogle Scholar