On the study of the eigenvalues, the numerical range and the numerical radius of linear operator in Hilbert space

Abstract

Our main goal in this thesis is to refine some well-known numerical radius inequalities of Operators on a Hilbert space.We provide some new bounds of the numerical radius for one Operator and for the off-diagonal parts of 2 x 2 operator matrices. Also, we establish several Upper and lower bounds for the Euclidean operator radius of two linear operators in complex Hilbert space.We apply these results to reobtain some well known inequalities for the classi- cal numerical radius. Finally, we give some bounds for the weighted numerical radius of one operator as well as for 2x2 operator matrices. We reobtain some well known inequalities for the classical numerical radius. New characterization for the weighted numerical radius is also given.