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A characterization of bilateral operator weighted shifts being Cowen-Douglas operators


Authors: You Qing Ji, Juexian Li and Yihua Yang
Journal: Proc. Amer. Math. Soc. 129 (2001), 3205-3210
MSC (2000): Primary 47B10, 47B37
DOI: https://doi.org/10.1090/S0002-9939-01-06031-2
Published electronically: May 21, 2001
MathSciNet review: 1844994
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Abstract:

It is characterized when a bilateral operator weighted shift is a Cowen-Douglas operator.


References [Enhancements On Off] (What's this?)

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  • [2] R. Gellar, Operators commuting with a weighted shift, Proc. Amer. Math. Soc., 23(1969), 538-545. MR 41:4277a
  • [3] C. Jiang and Z. Wang, Strongly irreducible operators on Hilbert space, Pitman Res. Notes Math. 389, Longman Sci. Tech., Harlow, Essex, 1998. MR 2000c:47033
  • [4] A. Lambert, Unitary equivalence and reducibility of invertibly weighted shifts, Bull Austral. Math. Soc., 5(1971), 157-173. MR 45:4196
  • [5] J. Li, Y. Ji and S. Sun, The essential spectrum and Banach reducibility of operator weighted shifts (in Chinese), it to appear in Acta Math. Sinica.
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Additional Information

You Qing Ji
Affiliation: Department of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email: jiyqji@public.cc.jl.cn

Juexian Li
Affiliation: Department of Mathematics, Liaoning University, Shenyang 110036, People’s Republic of China

Yihua Yang
Affiliation: Changchun Arts and Science College for Adults, Changchun 130000, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-01-06031-2
Keywords: Bilateral operator weighted shift, Cowen-Douglas operator
Received by editor(s): November 1, 1999
Published electronically: May 21, 2001
Additional Notes: The first author was supported by the National Natural Science Foundation of China (19901011).
The second author was supported by NEF of Liaoning Education Commission of China.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society

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