Convexity And Norm Estimation Of Special Operator Matrices

In the operator theory,the operator matrices have the important mathematical properties and applications.Hua-type operator matrices are special operator block matrices based on thoughts of mathematician L.K.Hua.Many scholars have stud-ied them and got many interesting results.In this thesis,by the variants of Hua-type operator matrices,the new operator matrices (?)n,(?)n,Uu(A,B)and GU(A,B)are defined and convex properties,the extreme points and norms of these operator ma-trices are obtained.This thesis is divided into three chapters,the concrete structure is as follows:Chapter 1 We will introduce the background and results of this thesis.Then,we will give relevant definitions,properties and theorems of Hua-type operator matrices.Chapter 2 First,we will prove (?)n = (?)n+1,(?)n = (?)n+1(n = 1,2,…);second,we will show that (?)n is a convex and compact set in the ω*topology.Then the norm bounds of (?)n and (?)n are investigated.Chapter 3 The positivity of HU(A,B)and GUτ(A,B)are shown,and also the minimum operator norm of HU(A,B)and GUτ(A,B)are given.Then,some equiva-lent conditions of the positivity of (?)uτ(A,B)and (?)U(A,B)are obtained respectively.