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

 

Characterization of chaotic order
and its application to furuta inequality


Authors: Masatoshi Fujii, Jian Fei Jiang and Eizaburo Kamei
Journal: Proc. Amer. Math. Soc. 125 (1997), 3655-3658
MSC (1991): Primary 47A63, 47B15
MathSciNet review: 1415586
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Abstract: In this note, we give a simple characterization of the chaotic order $\log A \ge \log B$ among positive invertible operators $A, B$ on a Hilbert space. As an application, we discuss Furuta's type operator inequality.


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Additional Information

Masatoshi Fujii
Affiliation: Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582, Japan
Email: mfujii@cc.osaka-kyoiku.ac.jp

Jian Fei Jiang
Affiliation: Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582, Japan; permanent address: Department of Basic Science and Technology, China Textile University, Shanghai, China, Postal code 200051

Eizaburo Kamei
Affiliation: Momodani Senior High School, Ikuno, Osaka 544, Japan
Address at time of publication: Maebashi Institute of Technology, Kamisadori, Maebashi, Gunma 371, Japan
Email: kamei@maebashi-it.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04057-4
PII: S 0002-9939(97)04057-4
Keywords: Positive operators, chaotic order, L\"{o}wner-Heinz inequality, Furuta inequality
Received by editor(s): July 16, 1996
Dedicated: Dedicated to Professor P. R. Halmos on his 80th Birthday
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society