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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$p$-hyponormality is not translation-invariant


Authors: Muneo Cho and Jun Ik Lee
Journal: Proc. Amer. Math. Soc. 131 (2003), 3109-3111
MSC (2000): Primary 47B20, 47B35
Published electronically: December 30, 2002
MathSciNet review: 1993220
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Abstract: In this note we provide an example of a semi-hyponormal Hilbert space operator $T$ for which $T-\lambda $ is not $p$-hyponormal for some $\lambda \in \mathbb{C}$ and all $0 < p \leq \frac{1}{2}$.


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Additional Information

Muneo Cho
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
Email: chiyom01@kanagawa-u.ac.jp

Jun Ik Lee
Affiliation: Department of Mathematics, SungKyunKwan University, Suwon 440-746, Korea
Email: jilee@math.skku.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06865-X
PII: S 0002-9939(02)06865-X
Keywords: Semi-hyponormal, $p$-hyponormal, paranormal, translation--invariant
Received by editor(s): February 14, 2000
Received by editor(s) in revised form: April 26, 2002
Published electronically: December 30, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society