ON INEQUALITIES OF SPECTRAL AND NUMERICAL RADIUS

Abstract

In this work, we study the concept of numerical range and numer ical radius for bounded linear operators on Hilbert space (both finite and infinite-dimensional) and to understand the relationship between these with the spectrum and the spectral radius, respectively. The main results are: determination of the numerical range for a two by two matrices, containment of the spectrum in the closure of the numerical range and inequalities involving numerical and spectral radius. Our aim is to know the geometry of a bounded linear oper ator with the help of spectrum and numerical range and the bounds of spectral and numerical radius.We also analyse to get an idea for numerical radius of sum and product of specific operators. And we continue the study with generalization of the numerical radius of a single and double operators.