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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 205-207
http://dx.doi.org/10.1155/S0161171295000263

Around the Furuta inequality—the operator inequalities (AB2A)¾ABAA3

Department of Mathematics, California State University, Long Beach 90840, California, USA

Received 21 July 1993; Revised 5 November 1993

Copyright © 1995 Hindawi Publishing Corporation. 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

For positive operators A and B with A invertible it is shown that (AB2A)½A2 implies (AB2A)¾ABA. The inequalities in the title for 0BA are then derived as a conquence.