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Remark on: ``Tridiagonal matrix representations of cyclic selfadjoint operators'' [Pacific J. Math. 114 (1984), no. 2, 325-334; MR0757504 (85h:47033)] by J. Dombrowski


Author: Peng Fan
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
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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 [Enhancements On Off] (What's this?)

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  • [2] J. Dombrowski, Tridiagonal matrix representations of cyclic self-adjoint operators, Pacific. J. Math. 114 (1984), 325-334. MR 757504 (85h:47033)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0848881-4
Keywords: Traces, shift operators
Article copyright: © Copyright 1986 American Mathematical Society

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