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Proceedings of the American Mathematical Society

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$p$-hyponormal operators are subscalar


Authors: Lin Chen, Ruan Yingbin and Yan Zikun
Journal: Proc. Amer. Math. Soc. 131 (2003), 2753-2759
MSC (2000): Primary 47B99, 47A10
Published electronically: April 7, 2003
MathSciNet review: 1974332
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Abstract: We prove that if $R, S\in B(\mathbf{X }), R, S$ are injective, then $RS$ is subscalar if and only if $SR$ is subscalar. As corollaries, it is shown that $p$-hyponormal operators $(0<p\le 1)$ and log-hyponormal operators are subscalar; also w-hyponormal operators $T$ with Ker$T\subset $ Ker$T^{*}$and their generalized Aluthge transformations $T(r, 1-r) (0<r<1)$ are subscalar.


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Additional Information

Lin Chen
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

Ruan Yingbin
Affiliation: Department of Mathematics, University of Xiamen, Xiamen, 361005, People’s Republic of China
Email: ruanyingbin@263.net

Yan Zikun
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07011-4
Keywords: Subscalar, $p$-hyponormal, log-hyponormal, w-hyponormal, Aluthge transformations
Received by editor(s): February 12, 2002
Published electronically: April 7, 2003
Additional Notes: This research was supported by the National Natural Science Foundation of China.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society