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Fuglede's Commutativity Theorem and ∩ R(T - λ)

Published online by Cambridge University Press:  20 November 2018

Robert Whitley
Robert Whitley*
Affiliation:
University of California Irvine, CA 92717
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Abstract

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Fuglede's commutativity theorem for normal operators is an easy consequence of the result that: For T normal, denoting the range of T - λ by R(T - λ), ∩ {R(T - λ) : all λ} = {0}:

Keywords

47B2047B15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 331 - 334
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Clancey, K., Seminormal Operators, Lecture Notes in Math #742, Springer-Verlag, New York, 1979.Google Scholar
2. Halmos, P., A Hilbert Space Problem Book, 2nd éd., Springer-Verlag, 1982.Google Scholar
3. Johnson, B., Continunity of linear operators commuting with continuous linear operators, Trans. A.M.S. 128 (1967), 88–102.Google Scholar
4. Johnson, B., and A. Sinclair, Continunity of linear operators commuting with continuous linear operators II, Trans. A.M.S. 146 (1969), 533–540.Google Scholar
5. Ptak, V., and P. Vrbova, On the spectral function of a normal operator, Czech. Math. J. 23 (1973), 615–616.Google Scholar
6. Putnam, C., Ranges of normal and subnormal operators, Mich. Math. J. 18 (1972), 33–36.Google Scholar
7. Putnam, C., Normal operators and strong limit approximations, Indiana Univ. Math. J. 32 (1983), 377– 379.Google Scholar
8. Sinclair, A., Automatic Continunity of Linear Operators Cambridge Univ. Press, Cambridge, 1976.Google Scholar
9. Stampfli, J., A local spectral theory for operators, J. Functional Analysis 4 (1969), 1–10.Google Scholar
10. Stampfli, J., A local spectral theory for operators II, Bull. Amer. Math. Soc. 75 (1969), 803–806.Google Scholar
11. Stampfli, J., A local spectral theory for operators III: resolvents, spectral sets, and similarity, Trans, Amer. Math. Soc. 168 (1972), pp. 133–151.Google Scholar
12. Stampfli, J., A local spectral theory for operators IV: Invariant subspaces, Indiana Univ. Math. J. 22 (1972), 159–167.Google Scholar
13. Stampfli, J., A local spectral theory for operators V: Spectral subspaces for hyponormal operators, Trans, Amer. Math. Soc. 217 (1976), 285–296.Google Scholar
14. Stampfli, J., and B. Wadha, An asymmetric Putnam-Fug le de theorem for dominant operators, Indiana Univ. Math. J. 25 (1976), 359–365.Google Scholar