本文選題：數(shù)值域 + 數(shù)值域半徑　； 參考：《曲阜師范大學》2016年碩士論文

【摘要】：本文主要研究了算子的q-數(shù)值域,這是對算子的數(shù)值域的結(jié)論的推廣.我們首先給出了算子的q-數(shù)值域及q-數(shù)值域半徑的定義,介紹了算子的q-數(shù)值域的基本性質(zhì),并給出算子的q-數(shù)值域的有關(guān)結(jié)論；然后介紹算子的q-數(shù)值域半徑的范數(shù)性質(zhì)和一些不等式;最后通過對W{0}={A∈B(H),0∈W(A)}的代數(shù)性質(zhì)推廣,給出了q-數(shù)值域情形下,Wq{0)={A∈B(H),0∈Wq(A)}的代數(shù)性質(zhì).根據(jù)內(nèi)容,本文分為以下三章.第一章首先給出了算子的數(shù)值域W(A)、算子的數(shù)值域半徑r(A)、算子的q-數(shù)值域Wq(A)、算子的q-數(shù)值域半徑rq(A)的定義,然后介紹了Wq(A)的有關(guān)結(jié)論,包括Wq(A)的凸性,q不同時,Wq(A)之間的關(guān)系,Wq(A)的刻畫以及Wq(A)的邊界.第二章研究了算子的q-數(shù)值域半徑rq(A)的范數(shù)性質(zhì)和一些不等式,并通過對r(A)的不等式進行推廣,給出了關(guān)于rq(A)的一些新的不等式.在第三章中,記W{0}={A ∈B(H),0 ∈W(A)},Wq{0}={A ∈B(H),0 ∈Wq(A)},通過對W{o}的代數(shù)性質(zhì)的推廣,給出Wq{0}的代數(shù)性質(zhì).
[Abstract]:In this paper, the q-numerical range of the operator is studied, which is a generalization of the conclusion of the numerical range of the operator. Firstly, we give the definitions of q-numerical region and q-numerical radius of operator, introduce the basic properties of q-numerical range of operator, and give some conclusions about q-numerical range of operator. Then we introduce the norm properties and some inequalities of the q-numerical radius of the operator, and finally, by generalizing the algebraic properties of W {0} = {A 鈭，

本文編號：1925101