Reducing decompositions for strictly cyclic operators
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- by Richard Bouldin PDF
- Proc. Amer. Math. Soc. 40 (1973), 477-481 Request permission
Abstract:
If $T$ is a strictly cyclic operator on $H$ then $H$ has a direct sum decomposition ${H_1} \oplus {H_2}$ where ${H_1}$ and ${H_2}$ are invariant under $T$ if and only if the spectrum of $T$ is not connected. If $\lambda$ is a reducing eigenvalue for the strictly cyclic operator $T$ then the multiplicity of $\lambda$ is one and $\lambda$ is an isolated point of the spectrum of $T$.References
- Sterling K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 13 (1962), 111–114. MR 133690, DOI 10.1090/S0002-9939-1962-0133690-8
- Richard Bolstein and Warren Wogen, Subnormal operators in strictly cyclic operator algebras, Pacific J. Math. 49 (1973), 7–11. MR 355670
- Mary R. Embry, Strictly cyclic operator algebras on a Banach space, Pacific J. Math. 45 (1973), 443–452. MR 318922
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473 R. L. Kelley, Weighted shifts on Hilbert space, Dissertation, University of Michigan, Ann Arbor, Mich., 1966.
- Alan Lambert, Strictly cyclic weighted shifts, Proc. Amer. Math. Soc. 29 (1971), 331–336. MR 275213, DOI 10.1090/S0002-9939-1971-0275213-4
- Alan Lambert, Strictly cyclic operator algebras, Pacific J. Math. 39 (1971), 717–726. MR 310664 —, Spectral properties of strictly cyclic operator algebras (preprint).
- Eric A. Nordgren, Closed operators commuting with a weighted shift, Proc. Amer. Math. Soc. 24 (1970), 424–428. MR 257786, DOI 10.1090/S0002-9939-1970-0257786-X
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 477-481
- MSC: Primary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320777-7
- MathSciNet review: 0320777