International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 205-207
doi:10.1155/S0161171295000263
Around the Furuta inequality—the operator inequalities (AB2A)¾≤ABA≤A3
Department of Mathematics, California State University, Long Beach 90840, California, USA
Received 21 July 1993; Revised 5 November 1993
Copyright © 1995 Derming Wang. 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)½≤A2 implies
(AB2A)¾≤ABA. The inequalities in the title for 0≤B≤A are then derived as a conquence.