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Isometric Images of C* Algebras

Published online by Cambridge University Press:  20 November 2018

Donal P. O’Donovan  and
Kenneth R. Davidson
Donal P. O’Donovan
Affiliation:
Mathematics Department, Trinity College, Dublin 2, Ireland
Kenneth R. Davidson
Affiliation:
Pure Mathematics Department, University of Waterloo, Canada
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Abstract

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It is shown that if the isometric image of a linear subspace of Hilbert space operators is irreducible in a strong sense, then the isometry is either a multiplicative or anti-multiplicative map, possibly followed by multiplication by a unitary.

Keywords

46L0547D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 286 - 294
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Arveson, W. B., An Invitation to C*-algebras. Springer-Verlag, 1976.Google Scholar
2. Dixmier, J., Les C*-algebres et leurs representations. Cahiers scientique fasc. 29, Gauthiers-Villars, Paris, 1964.Google Scholar
3. Halmos, P. R., A Hilbert space problem book. Van Nostrand, Princeton, N. J., 1967.Google Scholar
4. Hoffman, K., Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962.Google Scholar
5. Harris, L. A., Schwarz’s lemma in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 62(1969) 1014–1017.Google Scholar
6. Hopenwasser, A. and Plastiras, J., Isometries of Quasitriangular Operator Algebras, Proc. A.M.S. 65(1977) 242–244.Google Scholar
7. Kadison, R. V., Isometries of Operator Algebras, Ann. of Math., 54(1951) 325–338.Google Scholar
8. Paterson, A. and Sinclair, A., Characterization of isometries between C*-algebras, J. London Math. Soc. (5)2(1972) 755–761.Google Scholar
9. Störmer, E., Positive linear maps of Operator Algebras, Acta Math. 110(1963) 233–278.Google Scholar