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.

Computation of Generalized antieigenvalue pair of Right definite two-parameter eigenvalue problems

“…Many attempts have been made by the researchers over the years to compute approximate antieigenvalue and their associated antieigenvectors for operators on complex Hilbert spaces. In particular, numerical aspects of normal operators have been analyzed in (Gustafson & Rao, 1997;Seddighin & Gustafson, 2005;Seddighin, 2002Seddighin, , 2003Seddighin, , 2004Seddighin, , 2012Paul et al, 2015;Mirman, 1983), and the references therein. For matrix numerical computations have been reported in (Khattree, 2013).…”