(The) numerical range of the Jordan block on 3-dimensional space

Abstract

이 논문에서는 어떤 작용소 T의 numerical range의 여러 가지 성질들에 대하여 공부한다. 특히, 3차원 공간상에서 작용소 T의 Jordan form에 대한 numerical range를 특성화 한다;In this paper, we study some properties of numerical range for any operator T . In particular, we focus on the numerical ranges of Jordan forms of an operator T on a 3-dimensional space. This characterization depends on the diagonalization of an operator T on a 3-dimensional space. In fact, if T ∈ M_(3) and T_(J) is the Jordan form of T , we show that W(T_(J)) = conv(σ(T_(J))) when T is diagonalizable. Moreover we calculate several forms of the numerical ranges of a non-diagonalizable operator.