Journal of Inequalities and Applications 
Volume 4 (1999), Issue 4, Pages 339-344
doi:10.1155/S1025583499000442

A short proof of the best possibility for the grand Furuta inequality

Masatoshi Fujii,1 Akemi Matsumoto,2 and Ritsuo Nakamoto3

 1Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
2Higashi-Toyonaka Senior Highschool, Shinsenriminami, Toyonaka, Osaka 565-0084, Japan
3Faculty of Engineering, Ibaraki University, Nakanarusawa, Hitachi, Ibaraki 316-0033, Japan
Received 10 April 1999; Revised 9 May 1999

Abstract

In this note, we give a short proof to the best possibility for the grand Furuta inequality: for given p, s≥1, t∈[0,1], r≥t and α>1, there exist positive invertible operators S and T such that S≥T and S(1−t+r)α≧̸[Sr/2(S−t/2TpS−t/2)sSr/2]((1−t+r)/((p−t)s+r))α.