Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-28T02:04:47.732Z Has data issue: false hasContentIssue false
  • English
  • Français

Isomorphisms of some convolution algebras and their multiplier algebras

Published online by Cambridge University Press:  17 April 2009

U.B. Tewari  and
G.I. Gaudry
U.B. Tewari
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
G.I. Gaudry
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
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 G1 and G2 be two locally compact abelian groups and let 1 ≤ p ∞. We prove that G1 and G2 are isomorphic as topological groups provid∈d there exists a bipositive or isometric algebra isomorphism of M(Ap (G1)) onto M(Ap (G2)). As a consequence of this, we prove that G1 and G2 are isomorphic as topological groups provided there exists a bipositive or isometric algebra isomorphism of Ap (G1) onto Ap (G2). Similar results about the algebras L1 ∩ Lp and L1 ∩ C0 are also established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 321 - 335
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Gaudry, G.I., “Isomorphism of multiplier algebras”, Canad. J. Math. 20 (1968), 1165–1172.Google Scholar
[2]Glicksberg, Irving, “Homomorphisms of certain algebras of measures”, Pacific J. Math. 10 (1960), 167–191.Google Scholar
[3]Helson, Henry, “Isomorphisms of abelian group algebras”, Ark. Mat. 2 (1954), 475–487.CrossRefGoogle Scholar
[4]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonio analysis, Volume II (Die Grundlehren der mathematischen Wissenschaften, Band 152. Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar
[5]Larsen, Ronald, An introduction to the theory of multipliers (Die Grundlehren der mathematischen Wissenschaften, Band 175. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[6]Rudin, Walter, Fourier analysis on groups (Interscience, New York, London, 1962).Google Scholar
[7]Wendel, J.G., “Left centralizers and isomorphisms of group algebras”, Pacific J. Math. 2 (1952), 251–261.CrossRefGoogle Scholar