International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 2, Pages 129-133

Some inequalities in B(H)

C. Duyar1 and H. Seferoglu2

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 C. Duyar and H. Seferoglu. 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.


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,}.