International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57, Pages 3037-3043
Antieigenvalue inequalities in operator theory
Mathematics Department, Indiana University East, Richmond 47374-1289, IN, USA
Received 15 March 2004
Copyright © 2004 Morteza Seddighin. 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.
We will prove some inequalities among trigonometric quantities of
two and three operators. In particular, we will establish an
inequality among joint trigonometric quantities of two operators
and trigonometric quantities of each operator. As a corollary, we
will find an upper bound and a lower bound for the total joint
antieigenvalue of two positive operators in terms of the smallest
and largest eigenvalues of these operators.