Geometry of Numerical Range of Linear Operator Polynomial  

作　　者：Deyu WU Alatancang CHEN 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China [2]School of Mathematical Sciences,Inner Mongolia Normal University,Hohhot 010022,China

出　　处：《Chinese Annals of Mathematics,Series B》2025年第1期151-162,共12页数学年刊(B辑英文版)

基　　金：supported by the National Natural Science Foundation of China(No.11561048);the Natural Science Foundation of Inner Mongolia(No.2023MS01011)。

摘　　要：Let B(X)be the algebra of all bounded linear operators on a Hilbert space X.Consider an operator polynomial P(λ)=A_(m)λ^(m)+A_(m-1)λ^(m-1)+……-+A_(0),where Ai∈B(X),i=0,1,…,m.The numerical range of P(λ)is defined as W(P(λ))={λ∈C:(P(λ)x,x)=0 for some x≠0}.The main goal of this paper is to respond to an open problem proposed by professor Li,and determine general conditions on connectivity,convexity and spectral inclusion property of W(P(λ)).They also consider the relationship between operator polynomial numerical range and block numerical range.

关 键 词：Linear operator polynomial Numerical range Connectedness CONVEXITY Block numerical range 

分 类 号：O17[理学—数学]