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Isometric representation of M(G) on B(H)

Published online by Cambridge University Press:  18 May 2009

F. Ghahramani
F. Ghahramani
Affiliation:
Department of Mathematics, University for Teacher Education, 49, Mobarezan Avenue, Tehran, Iran.
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In a recent paper, E. Størmer, among other things, proves the existence of an isometric isomorphism from the measure algebra M(G) of a locally compact abelian group G into BB(L2(G)), ([6], Proposition 4.6). Here we give another proof for this result which works for non-commutative G as well as commutative G. We also prove that the algebra L1(G, λ), with λ the left (or right) Haar measure, is not isometrically isomorphic with an algebra of operators on a Hilbert space. The proofs of these two results are taken from the author's Ph.D. thesis [4], submitted to the University of Edinburgh before Størmer's paper. The author wishes to thank Dr. A. M. Sinclair for his help and encouragement.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 119 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

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