On quasi-affine transforms of unilateral shifts
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- by Katsutoshi Takahashi PDF
- Proc. Amer. Math. Soc. 100 (1987), 683-687 Request permission
Abstract:
It is shown that if a contraction $T$ is a quasiaffine transform of a unilateral shift of finite multiplicity, then both the approximate point spectrum and the essential spectrum of $T$ coincide with the unit circle.References
- H. Bercovici and K. Takahashi, On the reflexivity of contractions on Hilbert space, J. London Math. Soc. (2) 32 (1985), no. 1, 149–156. MR 813394, DOI 10.1112/jlms/s2-32.1.149
- Stuart Clary, Equality of spectra of quasi-similar hyponormal operators, Proc. Amer. Math. Soc. 53 (1975), no. 1, 88–90. MR 390824, DOI 10.1090/S0002-9939-1975-0390824-7
- John B. Conway, Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. MR 634507
- John B. Conway, On quasisimilarity for subnormal operators, Illinois J. Math. 24 (1980), no. 4, 689–702. MR 586807
- James A. Deddens, Intertwining analytic Toeplitz operators, Michigan Math. J. 18 (1971), 243–246. MR 283611
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
- William W. Hastings, Subnormal operators quasisimilar to an isometry, Trans. Amer. Math. Soc. 256 (1979), 145–161. MR 546912, DOI 10.1090/S0002-9947-1979-0546912-3
- Béla Sz.-Nagy, Diagonalization of matrices over $H^{\infty }$, Acta Sci. Math. (Szeged) 38 (1976), no. 3-4, 223–238. MR 435907
- Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
- Béla Sz.-Nagy and Ciprian Foias, Jordan model for contractions of class $C._{O}$, Acta Sci. Math. (Szeged) 36 (1974), 305–322. MR 372651
- Katsutoshi Takahashi, Contractions with the bicommutant property, Proc. Amer. Math. Soc. 93 (1985), no. 1, 91–95. MR 766534, DOI 10.1090/S0002-9939-1985-0766534-7
- Mitsuru Uchiyama, Contractions and unilateral shifts, Acta Sci. Math. (Szeged) 46 (1983), no. 1-4, 345–356. MR 739054
- Pei Yuan Wu, When is a contraction quasisimilar to an isometry?, Acta Sci. Math. (Szeged) 44 (1982), no. 1-2, 151–155. MR 660521 —, Contractions quasisimilar to an isometry, preprint.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 683-687
- MSC: Primary 47A65; Secondary 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1987-0894438-X
- MathSciNet review: 894438