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Isomorphisms of some Segal algebras and their multiplier algebras

Published online by Cambridge University Press:  17 April 2009

U.B. Tewari  and
K. Parthasarathy
U.B. Tewari
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, U.P., India.
K. Parthasarathy
Affiliation:
Department of Mathematics, University of Calicut, Calicut 673635, India.
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Abstract

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Let G1, G2, be locally compact groups and let S1, S2, be Segal algebras on G1, G2, respectively. Under certain conditions on G1, G2, and S1, S2, we prove that if there is a bipositive or isometric isomorphism between S1, S2, or between their multiplier algebras then G1, and G2, are topologically isomorphic.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 3 , June 1982 , pp. 441 - 451
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Brainerd, B. and Edwards, R.E., “Linear operators which commute with translations. Part I: Representation theorems”, J. Austral. Math. Soc. 6 (1966), 289–327.CrossRefGoogle Scholar
[2]Edwards, R.E., “Bipositive and isometric isomorphisms of some convolution algebras”, Canad. J. Math. 17 (1965), 839–846.CrossRefGoogle Scholar
[3]Gaudry, G.I., “Isomorphism of multiplier algebras”, Canad. J. Math. 20 (1968), 1165–1172.CrossRefGoogle Scholar
[4]Helson, Henry, “Isomorphisms of abelian group algebras”, Ark. Mat. 2 (1954), 475–487.CrossRefGoogle Scholar
[5]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, Volume II (Die Grundlehren der mathematischen Wissenschaften, 152. Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar
[6]Johnson, B.E., “Isometric isomorphisms of measure algebras”, Proc. Amer. Math. Soc. 15 (1964), 186–188.CrossRefGoogle Scholar
[7]Kawada, Yukiyoshi, “On the group ring of a topological group”, Math. Japon. 1 (1948), 1–5.Google Scholar
[8]Larsen, Ronald, An introduction to the theory of multipliers (Die Grundlehren der mathematischen Wissenschaften, 175. Springer-Verlag, Berlin, Heidelberg, New York, 1971).Google Scholar
[9]Nagrajan, Kasturi, “Multipliers of Segal algebras” (Doctoral thesis, Institute of Mathematical Sciences, Madras, 1976).Google Scholar
[10]Parrot, S.K., “Isometric multipliers”, Pacific J. Math. 25 (1968), 159–166.CrossRefGoogle Scholar
[11]Parthasarathy, K. and Tewari, U.B., “Isometric multipliers of Segal algebras”, Bull. Austral. Math. Soc. 20 (1979), 105–114.CrossRefGoogle Scholar
[12]Reiter, Hans, Classical harmonic analysis and locally compact groups (Clarendon Press, London, 1968).Google Scholar
[13]Reiter, Hans, L1-algebras and Segal algebras (Lecture Notes in Mathematics, 231. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[14]Rigelhof, Roger, “Norm decreasing homomorphisms of measure algebras”, Trans. Amer. Math. Soc. 136 (1969), 361–371.CrossRefGoogle Scholar
[15]Strichartz, Robert S., “Isometric isomorphisms of measure algebras”, Pacific J. Math. 15 (1965), 315–317.CrossRefGoogle Scholar
[16]Strichartz, Robert S., “Isomorphisms of group algebras”, Proc. Amer. Math. Soc. 17 (1966), 858–862.CrossRefGoogle Scholar
[17]Tewari, U.B., “Isomorphisms of some convolution algebras and their multiplier algebras”, Bull. Austral. Math. Soc. 7 (1972), 321–335.CrossRefGoogle Scholar
[18]Wendel, J.G., “On isometric isomorphism of group algebras”, Pacific J. Math. 1 (1951), 305–311.CrossRefGoogle Scholar
[19]Wendel, J.G., “Left centralizers and isomorphisms of group algebras”, Pacific J. Math. 2 (1952), 251–261.Google Scholar