Volume 4,  Issue 2, 2003

Article 40

REVERSE INEQUALITIES ON CHAOTICALLY GEOMETRIC MEAN VIA SPECHT RATIO, II

MASATOSHI FUJII, JADRANKA MICIC, J.E. PECARIC AND YUKI SEO

DEPARTMENT OF MATHEMATICS
OSAKA KYOIKU UNIVERSITY 
KASHIWARA, OSAKA 582-8582, JAPAN.
E-Mail: mfujii@cc.osaka-kyoiku.ac.jp

TECHNICAL COLLEGE ZAGREB 
UNIVERSITY OF ZAGREB
KONAVOSKA 2, 
10000 ZAGREB, CROATIA.
E-Mail: Jadranka.Micic@public.srce.hr

FACULTY OF TEXTILE TECHNOLOGY
UNIVERSITY OF ZAGREB
PIEROTTIJEVA 6
10000 ZAGREB, CROATIA.
E-Mail: pecaric@mahazu.hazu.hr
URL: http://mahazu.hazu.hr/DepMPCS/indexJP.html

TENNOJI BRANCH, SENIOR HIGH SCHOOL
OSAKA KYOIKU UNIVERSITY
TENNOJI, OSAKA 543-0054, JAPAN.
E-Mail: yukis@cc.osaka-kyoiku.ac.jp

Received 24 January, 2003; Accepted 5 March, 2003.
Communicated by: S. Saitoh

ABSTRACT.   In 1967, as a converse of the arithmetic-geometric mean inequality, Mond and Shisha gave an estimate of the difference between the arithmtic mean and the geometric one, which we call it the Mond-Shisha difference. As an application of Mond-Pecaric method, we show some order relations between the power means of positive operators on a Hilbert space. Among others, we show that the upper bound of the difference between the arithmetic mean and the chaotically geometric one of positive operators coincides with the Mond-Shisha difference.
Key words:
Operator concavity, Power mean, Arithmetic mean, Geometric mean.

2000 Mathematics Subject Classification:
Primary 47A30, 47A63.

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