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Harmonic analysis on the Fourier algebras A1, p(G)

Part of: Abstract harmonic analysis Commutative Banach algebras and commutative topological algebras Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Hang-Chin Lai  and
Ing-Sheun Chen
Hang-Chin Lai
Affiliation:
Institute of Mathematics, National Tsing Hua University Hsinchu, Taiwan
Ing-Sheun Chen
Affiliation:
Department of Applied Mathematics, Fengchia University, Taichung, Taiwan
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Abstract

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Let G be a locally compact group G (which may be non-abelian) and Ap(G) the p-Fourier algebra of Herz (1971). This paper is concerned with the Fourier algebra Al, p(G) = Ap(G) ∩ L1(G) and various relations that exist between Al, p(G), Ap(G) and G.

Keywords

Banach algebraFourier algebraamenable groupfactorization propertyweak factorization propertymultiplier

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc. 46H10: Ideals and subalgebras 46H20: Structure, classification of topological algebras 46J20: Ideals, maximal ideals, boundaries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 4 , April 1981 , pp. 438 - 452
Copyright
Copyright © Australian Mathematical Society 1981

References

Burnham, J. T. (1972), ‘Closed ideals in subalgebras of Banach algebras’, Proc. Amer. Math. Soc. 32, 551–555.CrossRefGoogle Scholar
Cohen, P. J. (1959), ‘Factorization in group algebras’, Duke Math. J. 26, 199–205.Google Scholar
Eymard, P. (1964), ‘L'algebra de Fourier d'un group localement compact’, Bull. Soc. Math. France 92, 181–236.Google Scholar
Eymard, P. (1971), Algebras Ap et convoluteurs de Lp, Seminaire Bourbaki, 367 (1969/1970), pp. 55–72 (Lecture Notes in Mathematics 180, Springer-Verlag).Google Scholar
Figà-Talamanca, A. (1964), ‘Multipliers of p-integrable functions’ Bull. Amer. Math. Soc. 70, 666–669.Google Scholar
Herz, C. (1971), ‘The theory of p-spaces with an application to convolution operators’, Trans. Amer. Math. Soc. 154, 69–82.Google Scholar
Herz, C. (1973), ‘Harmonic synthesis for subgroups’, Ann. Inst. Fourier (Grenoble) 23, 91–123.Google Scholar
Lai, H. C. (1969), ‘On some properties of AP(G)-algebras’, Proc. Japan Acad. 45, 572–576.Google Scholar
Lai, H. C. (1970), ‘Remark on the AP(G)-algebras’, Proc. Japan Acad. 46, 58–63.Google Scholar
Lai, H. C. (1975), ‘Banach algebras which are ideals in a Banach algebra’, Bull. Inst. Math. Acad. Sinica. 3, 383–389.Google Scholar
Larsen, R. (1971), An introduction to the theory of multipliers (Springer-Verlag, Berlin Herdelberg, New York).Google Scholar
Loomis, L. H. (1953), An introduction to abstract harmonic analysis (Van Nostrand Company, New York).Google Scholar
Porcelli, P. (1966), Linear spaces of analytic functions (McGraw-Hill, New York).Google Scholar
Varopoulos, N. Th. (1964), ‘Sur les forms positives d'une algebra de Banach’, C. R. Acad. Sci. Paris Ser. A 258, 2465–2467.Google Scholar
Wang, H. C. (1972), ‘Nonfactorization in group algebras’, Studia Math. 42, 231–241.CrossRefGoogle Scholar
Yap, L. Y. H. (1970), ‘Ideals in subalgebras of the group algebras’, Studia Math. 40, 165–175.Google Scholar
Wang, J. K. (1961), ‘Multipliers of commutative Banach algebras’, Pacific J. Math. 11, 1131–1149.Google Scholar