Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-04T12:13:57.188Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

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.

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

REFERENCES

1.Berberian, S. K., Lectures in functional analysis and operator theory (Springer Verlag, 1973).Google Scholar
2.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Note Series 2 (Cambridge, 1971).Google Scholar
3.Busby, R. C., Double centralizers and extensions of C*-algebras, Trans. Atner. Math. Soc. 132 (1968), 79–99.Google Scholar
4.Ghahramani, F., Homomorphisms and derivations on weighted convolution algebras, Ph.D. 'thesis, University of Edinburgh (05 1978).Google Scholar
5.Hewitt, E., and Ross, K. A., Abstract harmonic analysis, Vol. 1 (Springer-Verlag, 1963).Google Scholar
6.Størmer, E., Regular abelian Banach algebras of linear maps of operator algebras, J. Functional Analysis, 37 (1980), 331–373.Google Scholar
7.Wendel, J. G., Left centralizers and isomorphisms of group algebras, Pacific J. Math. 92 (1952), 251–261.Google Scholar
8.Young, N. J., The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. 2, 24 (1973), 59–62.Google Scholar