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
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
Copyright © 1999 Masatoshi Fujii et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.