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On $p$-hyponormal operators

Author(s): Eungil Ko
Journal: Proc. Amer. Math. Soc. 128 (2000), 775-780.
MSC (2000): Primary 47B20, 47A15
Posted: October 20, 1999
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Abstract | References | Similar articles | Additional information

Abstract: In this paper we show that $p$-hyponormal operators with $0 \notin \sigma(|T|_{r}^{\frac{1}{2}})$ are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.

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J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. 52(1989), 562-570. MR 90h:47016

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E. Ko, On a Clary theorem, Bull.Kor.Math.Soc. 33(1996), 29-33. MR 97e:47031

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M. Martin and M. Putinar, Lectures on Hyponormal Operators, Birkhäuser Verlag, Boston, Vol. 39, 1989. MR 91c:47041

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M. Putinar, Hyponormal operators are subscalar, J. Op. Th. 12(1984), 385-395. MR 85h:47027

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W. Rudin, Functional Analysis, McGraw-Hill Int. Ed., 2nd Ed., 1991. MR 92k:46001

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D. Xia, Spectral Theory of Hyponormal Operators, Birkhäuser Verlag, Boston, 1983. MR 87j:47036

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Additional Information:

Eungil Ko
Affiliation: Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email: eiko@mm.ewha.ac.kr

DOI: 10.1090/S0002-9939-99-05600-2
PII: S 0002-9939(99)05600-2
Keywords: $p$-hyponormal, subscalar operators, invariant subspaces
Received by editor(s): April 22, 1998
Posted: October 20, 1999
Additional Notes: The author is supported by the MOST through National R & D Program (97-N6-01-01-A-5) for Women's Universities.
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society

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