Remark on: “Tridiagonal matrix representations of cyclic selfadjoint operators” [Pacific J. Math. 114 (1984), no. 2, 325–334; MR0757504 (85h:47033)] by J. Dombrowski
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Abstract:
In [2], Dombrowski used a "orthogonal polynomials" technique to obtain a sufficient condition (in terms of the weights) for the existence of an absolutely continuous subspace for real parts of unilateral weighted shifts. The purpose of this note is to present a "diagonal" technique that produces a trace criterion for the existence of an absolutely continuous subspace for real parts as well as unitary parts of (bounded) operators.References
- R. W. Carey and J. D. Pincus, Unitary equivalence modulo the trace class for self-adjoint operators, Amer. J. Math. 98 (1976), no. 2, 481–514. MR 420323, DOI 10.2307/2373898
- Joanne Dombrowski, Tridiagonal matrix representations of cyclic selfadjoint operators, Pacific J. Math. 114 (1984), no. 2, 325–334. MR 757504, DOI 10.2140/pjm.1984.114.325
- Peng Fan, On the diagonal of an operator, Trans. Amer. Math. Soc. 283 (1984), no. 1, 239–251. MR 735419, DOI 10.1090/S0002-9947-1984-0735419-8
- Peng Fan, Cartesian and polar decompositions of hyponormal operators, Math. Z. 188 (1985), no. 4, 485–492. MR 774553, DOI 10.1007/BF01161652 P. R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicities, Chelsea, New York, 1951.
- C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag New York, Inc., New York, 1967. MR 0217618, DOI 10.1007/978-3-642-85938-0
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 85-88
- MSC: Primary 47A65; Secondary 47B15, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1986-0848881-4
- MathSciNet review: 848881