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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.
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Abstract

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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

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