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Weyl's theorem holds for algebraically hyponormal operators

Author(s): Young Min Han; Woo Young Lee
Journal: Proc. Amer. Math. Soc. 128 (2000), 2291-2296.
MSC (2000): Primary 47A10, 47A53; Secondary 47B20
Posted: March 29, 2000
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Abstract:

In this note it is shown that if $T$ is an ``algebraically hyponormal" operator, i.e., $p(T)$ is hyponormal for some nonconstant complex polynomial $p$, then for every $f\in H(\sigma (T))$, Weyl's theorem holds for $f(T)$, where $H(\sigma (T))$ denotes the set of analytic functions on an open neighborhood of $\sigma (T)$.

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Additional Information:

Young Min Han
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

Woo Young Lee
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Email: wylee@yurim.skku.ac.kr

DOI: 10.1090/S0002-9939-00-05741-5
PII: S 0002-9939(00)05741-5
Keywords: Weyl's theorem, algebraically hyponormal operators, unilateral weighted shifts
Received by editor(s): August 22, 1998
Posted: March 29, 2000
Additional Notes: This work was partially supported by the BSRI-97-1420 and the KOSEF through the GARC at Seoul National University.
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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