Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T07:07:27.053Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructions of the maximal strongly character invariant segal algebras and their applications

Part of: Abstract harmonic analysis Locally compact abelian groups

Published online by Cambridge University Press:  09 April 2009

Chang-Pao Chen
Chang-Pao Chen
Affiliation:
Institute of Mathematics National Tsing Hua UniversityHsinchu, Taiwan 300 Republic of, China
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 G denote any locally compact abelian group with the dual group Γ. We construct a new kind of subalgebra L1(G) ⊗ΓS of L1(G) from given Banach ideal S of L1(G). We show that L1(G) ⊗гS is the larger amoung all strongly character invariant homogeneous Banach algebras in S. when S contains a strongly character invariant Segal algebra on G, it is show that L1(G) ⊗гS is also the largest among all strongly character invariant Segal algebras in S. We give applications to characterizations of two kinds of subalgebras of L1(G)-strongly character invariant Segal algebras on G and Banach ideal in L1(G) which contain a strongly character invariant Segal algebra on G.

Keywords

Banach idealhomogeneous Banach algebraSegal algebrastrongly character invariantlocally compact abelian group.

MSC classification

Secondary: 22B10: Structure of group algebras of LCA groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 1 , August 1983 , pp. 123 - 131
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Chen, C. P., ‘On the intersections and the unions of Banach algebras’, Tamkang J. Math. 9 (1978), 21–27.Google Scholar
[2]Cigler, J., ‘Normed ideals in L1(G)’, Nederl. Akad. Wetensch, Indag. Math. 31 (1969), 273–282.CrossRefGoogle Scholar
[3]Feichtinger, H. G., ‘Multipliers from L1(G) to a homogeneous Banach space,’ J. Math. Anal. Appl. 61 (1977), 341–356.Google Scholar
[4]Goldberg, R. R., Recent results on Segal algebras (Springer-Verlag, Lecture Notes in Math. 399, 1974).CrossRefGoogle Scholar
[5]Hewitt, E. and Ross, K. A., Abstract harmonic analysis (Springer-Verlag, New York, I (1963), II (1970)).Google Scholar
[6]Katznelson, Y., An introduction to harmonic analysis (Wiley, New York, 1968).Google Scholar
[7]Losert, V., ‘A characterization of the minimal strongly character invariant Segal algebra’, Ann. Inst. Fourier 30 (1980), 129–139.CrossRefGoogle Scholar
[8]Reiter, H., Classical harmonic analysis and locally compact groups (Oxford Mathematical Monographs, Oxford University Press, 1968).Google Scholar
[9]Reiter, H., L1-algebras and Segal algebras (Lecture Notes in Math. No. 231, Springer-Verlag, Berlin, 1971).Google Scholar
[10]Riemersma, M., ‘On some properties of normed ideals in L1(G)’, Nederl. Akad. Wetensch. Proc. Ser. A78 = Indag. Math. 37 (1975), 265–272.Google Scholar
[11]Rudin, W., Fourier analysis on groups (Interscience, New York, 1962).Google Scholar
[12]Wang, H. C., ‘Nonfactorization in group algebras’, Studia Math. 42 (1972), 231–241.CrossRefGoogle Scholar
[13]Wang, H. C., Homogeneous Banach algebras (Lecture Notes in Pure and Appl. Mathematics, Dekker, New York, 1977).Google Scholar