On the Numerical Range for Linear Operators in Hilbert Space

Abstract

numerical range W(T)의 개념을 사용하여 W(T)와 작용소 T의 어떤 spectrum들과의 관계를 보이고 나아가 그들 성질들로 부터 normal인 작용소를 찾아, W(T)의 extreme point와 Hilbert space의 선형 작용소의 spectrum들의 특성들을 살펴본다.

Using the concept of the numerical range W(T) of a linear operator T in Hilbert space H, we show the relations between W(T) and some spectrums of T. Moreover, their properties reduce a non-normal operator to a normal operator. Finally, we investigate the properties of an extreme point of W(T) and some spectrums of linear operators in Hilbert space.

Using the concept of the numerical range W(T) of a linear operator T in Hilbert space H, we show the relations between W(T) and some spectrums of T. Moreover, their properties reduce a non-normal operator to a normal operator. Finally, we investigate the properties of an extreme point of W(T) and some spectrums of linear operators in Hilbert space.