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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 57, Pages 3037-3043

Antieigenvalue inequalities in operator theory

Mathematics Department, Indiana University East, Richmond, IN 47374-1289, USA

Received 15 March 2004

Copyright © 2004 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.


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.