Journal of Inequalities and Applications 
Volume 2 (1998), Issue 2, Pages 149-156
doi:10.1155/S1025583498000095

A characterization of chaotic order and a problem

Masatoshi Fujii,1 Jian Fei Jiang,2 EiZaburo Kamei,3 and Kotaro Tanahashi4

 1Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582, Japan
2Department of Basic Science and Technology, China Textile University, Postal code 200051, Shanghai, China
3Maebashi Institute of Technology, Kamisadori, Gunma, Maebashi 371, Japan
4Department of Mathematics, Tohoku College of Pharmacy, Komatsushima, Aoba-ku, Sendai 981, Japan
Received 31 January 1997; Revised 23 April 1997

Abstract

In our previous notes, we give a useful characterization of the chaotic order, i.e., logA≥logB for positive invertible operators A and B . In this note, we present a short proof to the characterization of the chaotic order and give an answer to a related problem on it. Moreover we consider the orders defined by Aδ≥B​δ(0<δ<1) as an interpolation between the chaotic order and the usual order via the Furuta inequality.