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

DOI:
https://doi.org/10.1090/S0002-9939-97-04057-4

MathSciNet review:
1415586

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we give a simple characterization of the chaotic order among positive invertible operators on a Hilbert space. As an application, we discuss Furuta's type operator inequality.

**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,*assures for with*, 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****7.**E.Kamei,*A satellite to Furuta's inequality*, Math. Japon.,**33**(1988), 883-886. MR**89m:47011****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:
https://doi.org/10.1090/S0002-9939-97-04057-4

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