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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A condition under which $ B=A=U^*BU$ follows from $ B\le A\le U^*BU$

Author(s): Takateru Okayasu; Yasunori Ueta
Journal: Proc. Amer. Math. Soc. 135 (2007), 1399-1403.
MSC (2000): Primary 47A63; Secondary 47A10, 47A30
Posted: October 27, 2006
MathSciNet review: 2276648
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Abstract | References | Similar articles | Additional information

Abstract: We will give some sufficient conditions for a $ p$-hyponormal operator, $ p>0$, to be normal, and a sufficient condition for a triplet of operators $ A$, $ B$, $ U$ with $ A$, $ B$ self-adjoint and $ U$ unitary such that $ B\le A\le U^*BU$ necessarily satisfies $ B=A=U^*BU$.

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M. Chô and M. Itô, Putnum's inequality for $ p$-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2435-2440. MR 1246519 (95j:47027)

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T. Okayasu and Y. Ueta, Some order-like relations concerned with unitary equivalence, to appear.

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C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323-330. MR 0270193 (42:5085)

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D. Xia, Spectral theory of hyponormal operators, Birkhäuser Verlag, Basel, 1983. MR 0806959 (87j:47036)

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Additional Information:

Takateru Okayasu
Affiliation: Faculty of Science, Yamagata University, Yamagata 990-8560, Japan

Yasunori Ueta
Affiliation: Graduate School of Science and Engineering, Yamagata University, Yamagata 990-8560, Japan

DOI: 10.1090/S0002-9939-06-08595-9
PII: S 0002-9939(06)08595-9
Keywords: Hyponormal operators, Putnum's inequality, normal approximate point spectra.
Received by editor(s): August 17, 2005
Received by editor(s) in revised form: December 1, 2005
Posted: October 27, 2006
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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