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ISSN 1088-6826(e) ISSN 0002-9939(p)

Characterization of chaotic order and its application to furuta inequality

Author(s): Masatoshi Fujii; Jian Fei Jiang; 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.

References:

1.: T.Ando, On some operator inequalities, Math. Ann., 279 (1987), 157-159. MR 89c:47019
2.: M.Fujii, Furuta's inequality and its mean theoretic approach, J. Operator theory, 23 (1990), 67-72. MR 91g:47012
3.: M.Fujii,T.Furuta and E.Kamei, Operator functions associated with Furuta's inequality, Linear Alg. and its Appl., 179 (1993), 161-169. MR 93j:47026
4.: M.Fujii and E.Kamei, Furuta's inequality and a generalization of Ando's Theorem, Proc. Amer. Math. Soc., 115 (1992), 409-413. MR 92i:47018
5.: T.Furuta, $A \ge B \ge 0$ assures $(B^{r}A^{p}B^{r})^{1/q} \ge B^{(p+2r)/q}$ for $r \ge 0, p \ge 0, q \ge 1$ with $(1+2r)q \ge p+2r$ , Proc. Amer. Math. Soc., 101 (1987), 85-88. MR 89b:47028
6.: T.Furuta, Elementary proof of an order preserving inequality, Proc. Japan Acad., 65 (1989), 126. MR 90g:47029
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8.: G.K.Pedersen, Some operator monotone functions, Proc. Amer. Math. Soc., 36 (1972), 309-310. MR 46:6078

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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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