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


Authors: Takateru Okayasu and Yasunori Ueta
Journal: Proc. Amer. Math. Soc. 135 (2007), 1399-1403
MSC (2000): Primary 47A63; Secondary 47A10, 47A30
DOI: https://doi.org/10.1090/S0002-9939-06-08595-9
Published electronically: October 27, 2006
MathSciNet review: 2276648
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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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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: https://doi.org/10.1090/S0002-9939-06-08595-9
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
Published electronically: October 27, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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