摘要
本文主要讨论两个有界线性算子的联合数值域的凸性,对具有凸的联合数值域的算子对给了一个必要性条件.特别地,对二维Hilbert 空间上算子对的联合数值域之凸性给出了充要条件.
The main objective of this paper is to study the convexity of the joint numericalrange of two bounded linear operators and give a necessary condition for a pair ofoperators with convex joint numerical range.In particular,the paper shows a suffi-cient and necessary condition for the convexity of the joint numerical range of a pairof operators on 2-dim.Hilbert space.
关键词
有界线
算子
联合数值域
凸集
Hilbert space
a pair of linear operators
joint numerical range
convex set
