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International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 2, Pages 129-133
http://dx.doi.org/10.1155/S0161171201004458

Some inequalities in B(H)

1University of Ondokuz Mayis, Faculty of Art and Sciences, Department of Mathematics, Samsun, Turkey
2100. Yil University, Faculty of Education, Department of Mathematics, Van, Turkey

Received 1 December 1998; Revised 15 November 1999

Copyright © 2001 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

Let H denote a separable Hilbert space and let B(H) be the space of bounded and linear operators from H to H. We define a subspace Δ(A,B) of B(H), and prove two inequalities between the distance to Δ(A,B) of each operator T in B(H), and the value sup{AnTBnT:n=1,2,}.