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Characterizations of commutativity for C*-algebras

Published online by Cambridge University Press:  18 May 2009

M. J. Crabb ,
J. Duncan  and
C. M. McGregor
M. J. Crabb
Affiliation:
University of Glasgow
J. Duncan
Affiliation:
University of Stirling
C. M. McGregor
Affiliation:
University of Glasgow
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Let be a C*-algebra acting on the Hilbert space H and let be the self-adjoint elements of . The following characterization of commutativity is due to I. Kaplansky (see Dixmier [3, p. 58]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 2 , September 1974 , pp. 172 - 175
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Notes Series No. 2, 1971.CrossRefGoogle Scholar
2.Bouldin, R., The numerical range of a product, II, J. Math. Anal. Appl. 33 (1971), 212–219.CrossRefGoogle Scholar
3.Dixmier, J., Les C*-algèbres et leurs représentations, 2me edition (Paris, 1969).Google Scholar
4.Fukamiya, M., Misonou, M. and Takeda, Z., On order and commutativity of B*-algebras, Tôhoku Math. J. (2) 6 (1954), 89–93.CrossRefGoogle Scholar
5.Ogasawara, T., A theorem on operator algebras, J. Sci. Hiroshima Univ. Ser. A. 18 (1955), 307–309.Google Scholar
6.Sherman, S., Order in operator algebras, Amer. J. Math. 73 (1951), 227–232.Google Scholar
7.Taylor, D. C., The strict topology for double centralizer algebras, Trans. Amer. Math. Soc. 150 (1970), 633–643.CrossRefGoogle Scholar