本文關(guān)鍵詞：關(guān)于幾類特殊循環(huán)算子的研究　出處：《山東師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： ω循環(huán)代數(shù) 塊ω循環(huán)算子矩陣 同構(gòu)算子 泛函方程 范數(shù)估計(jì)

【摘要】：本文主要以斜循環(huán)矩陣,ω循環(huán)矩陣,塊ω循環(huán)矩陣,塊R循環(huán)矩陣和塊左循環(huán)矩陣為對(duì)象研究了這五類矩陣的相關(guān)問(wèn)題,如算子同構(gòu)問(wèn)題,范數(shù)估計(jì)問(wèn)題等.本文的主要內(nèi)容分為以下四個(gè)章節(jié)：第一章分為三小節(jié),第一節(jié)介紹了斜循環(huán)矩陣,ω循環(huán)矩陣,塊ω循環(huán)矩陣,塊R循環(huán)矩陣和塊左循環(huán)矩陣的應(yīng)用背景以及國(guó)內(nèi)外的研究現(xiàn)狀.第二節(jié)給出了這幾類特殊矩陣的定義、幾類特殊弱酉不變范數(shù)和重要的引理等相關(guān)知識(shí).第三節(jié)簡(jiǎn)單地介紹了本文的主要工作.第二章分為兩小節(jié),主要考慮了斜循環(huán)代數(shù)和ω循環(huán)代數(shù)上的同構(gòu)算子和泛函方程.第一小節(jié)首先介紹了斜循環(huán)代數(shù)上的冪等基,其次結(jié)合給出的冪等基構(gòu)造線性整函數(shù),又根據(jù)該線性整函數(shù)的性質(zhì)定義了與斜循環(huán)代數(shù)同構(gòu)的函數(shù)算子,并提出了函數(shù)算子的性質(zhì).最后給出了其他斜循環(huán)代數(shù)的性質(zhì)和一個(gè)線性對(duì)合.第二小節(jié)對(duì)第一小節(jié)的內(nèi)容作了推廣,將斜循環(huán)代數(shù)推廣到了ω循環(huán)代數(shù),研究了ω循環(huán)代數(shù)的冪等基,泛函方程,其他ω循環(huán)代數(shù),并給出一個(gè)線性對(duì)合.第三章分為三小節(jié),主要研究了塊ω循環(huán)矩陣,塊R循環(huán)矩陣和塊左循環(huán)矩陣的范數(shù)估計(jì),其中,ω=eiθ(0≤θ27π),R是一個(gè)非奇異酉矩陣.在C*-代數(shù)上定義了算子矩陣.在第一節(jié)中根據(jù)塊ω循環(huán)算子矩陣的可對(duì)角化,利用弱酉不變范數(shù)獲得了范數(shù)等式,并通過(guò)構(gòu)建特殊的酉矩陣將一般的塊算子矩陣和塊ω循環(huán)算子矩陣相聯(lián)系,結(jié)合拼擠型不等式的性質(zhì),得到了塊ω循環(huán)算子矩陣的范數(shù)不等式.在第二節(jié)中根據(jù)塊R循環(huán)算子矩陣的特殊結(jié)構(gòu),弱酉不變范數(shù)的不變性質(zhì)和拼擠型不等式的性質(zhì),研究了塊R循環(huán)算子矩陣的范數(shù)估計(jì).第三節(jié)中給出了塊左循環(huán)算子矩陣的范數(shù)估計(jì).第四章總結(jié)了本文的主要工作,并給出了相關(guān)內(nèi)容的一些建議和展望.
[Abstract]:In this paper, we study the problems of skew cyclic matrix, 蠅 cyclic matrix, block 蠅 cyclic matrix, block R cyclic matrix and block left cyclic matrix, such as operator isomorphism. The main contents of this paper are as follows: the first chapter is divided into three sections. In the first section, we introduce skew cyclic matrix, 蠅 cyclic matrix and block 蠅 cyclic matrix. The application background of block R cyclic matrix and block left cyclic matrix and the current research situation at home and abroad. In the second section, the definitions of these special matrices are given. Some special weak unitary invariant norms and important Lemma and other related knowledge. The third section briefly introduces the main work of this paper. The second chapter is divided into two sections. The isomorphic operators and functional equations on skew cyclic algebras and 蠅 -cyclic algebras are considered. In the first section, the idempotent bases on skew cyclic algebras are introduced, and the linear integral functions are constructed by combining the given idempotent bases. The function operator isomorphic to oblique cyclic algebra is defined according to the properties of the linear entire function. Finally, the properties of other oblique cyclic algebras and a linear involution are given. In the second section, the contents of the first section are generalized, and the skew cyclic algebras are extended to 蠅 cyclic algebras. In this paper, the idempotent basis, functional equation and other 蠅 -cyclic algebras of 蠅 -cyclic algebras are studied, and a linear involution is given. The third chapter is divided into three sections, and the block 蠅 -cyclic matrices are studied. The norm estimates of block R circulant matrix and block left cyclic matrix, where 蠅 ei 胃 0 鈮，

本文編號(hào)：1418893