Geodesic
Isometric representation of M(G) on B(H)
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 119-122

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Ghahramani, F. Isometric representation of M(G) on B(H). Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 119-122. doi: 10.1017/S0017089500004882
@article{10_1017_S0017089500004882,
     author = {Ghahramani, F.},
     title = {Isometric representation of {M(G)} on {B(H)}},
     journal = {Glasgow mathematical journal},
     pages = {119--122},
     year = {1982},
     volume = {23},
     number = {2},
     doi = {10.1017/S0017089500004882},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004882/}
}
TY  - JOUR
AU  - Ghahramani, F.
TI  - Isometric representation of M(G) on B(H)
JO  - Glasgow mathematical journal
PY  - 1982
SP  - 119
EP  - 122
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004882/
DO  - 10.1017/S0017089500004882
ID  - 10_1017_S0017089500004882
ER  - 
%0 Journal Article
%A Ghahramani, F.
%T Isometric representation of M(G) on B(H)
%J Glasgow mathematical journal
%D 1982
%P 119-122
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004882/
%R 10.1017/S0017089500004882
%F 10_1017_S0017089500004882

[1] 1.Berberian, S. K., Lectures in functional analysis and operator theory (Springer Verlag, 1973). Google Scholar

[2] 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] 3.Busby, R. C., Double centralizers and extensions of C*-algebras, Trans. Atner. Math. Soc. 132 (1968), 79–99. Google Scholar

[4] 4.Ghahramani, F., Homomorphisms and derivations on weighted convolution algebras, Ph.D. 'thesis, University of Edinburgh (05 1978). Google Scholar

[5] 5.Hewitt, E., and Ross, K. A., Abstract harmonic analysis, Vol. 1 (Springer-Verlag, 1963). Google Scholar

[6] 6.Størmer, E., Regular abelian Banach algebras of linear maps of operator algebras, J. Functional Analysis, 37 (1980), 331–373. Google Scholar

[7] 7.Wendel, J. G., Left centralizers and isomorphisms of group algebras, Pacific J. Math. 92 (1952), 251–261. Google Scholar

[8] 8.Young, N. J., The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. 2, 24 (1973), 59–62. Google Scholar

Cité par Sources :