International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57-60, Pages 3037-3043
doi:10.1155/S0161171204403615

Antieigenvalue inequalities in operator theory

Abstract

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.