关于几类特殊循环算子的研究

发布时间：2018-01-13 12:52

  本文关键词：关于几类特殊循环算子的研究　出处：《山东师范大学》2015年硕士论文　论文类型：学位论文

  更多相关文章： ω循环代数 块ω循环算子矩阵 同构算子 泛函方程 范数估计

【摘要】：本文主要以斜循环矩阵,ω循环矩阵,块ω循环矩阵,块R循环矩阵和块左循环矩阵为对象研究了这五类矩阵的相关问题,如算子同构问题,范数估计问题等.本文的主要内容分为以下四个章节：第一章分为三小节,第一节介绍了斜循环矩阵,ω循环矩阵,块ω循环矩阵,块R循环矩阵和块左循环矩阵的应用背景以及国内外的研究现状.第二节给出了这几类特殊矩阵的定义、几类特殊弱酉不变范数和重要的引理等相关知识.第三节简单地介绍了本文的主要工作.第二章分为两小节,主要考虑了斜循环代数和ω循环代数上的同构算子和泛函方程.第一小节首先介绍了斜循环代数上的幂等基,其次结合给出的幂等基构造线性整函数,又根据该线性整函数的性质定义了与斜循环代数同构的函数算子,并提出了函数算子的性质.最后给出了其他斜循环代数的性质和一个线性对合.第二小节对第一小节的内容作了推广,将斜循环代数推广到了ω循环代数,研究了ω循环代数的幂等基,泛函方程,其他ω循环代数,并给出一个线性对合.第三章分为三小节,主要研究了块ω循环矩阵,块R循环矩阵和块左循环矩阵的范数估计,其中,ω=eiθ(0≤θ27π),R是一个非奇异酉矩阵.在C*-代数上定义了算子矩阵.在第一节中根据块ω循环算子矩阵的可对角化,利用弱酉不变范数获得了范数等式,并通过构建特殊的酉矩阵将一般的块算子矩阵和块ω循环算子矩阵相联系,结合拼挤型不等式的性质,得到了块ω循环算子矩阵的范数不等式.在第二节中根据块R循环算子矩阵的特殊结构,弱酉不变范数的不变性质和拼挤型不等式的性质,研究了块R循环算子矩阵的范数估计.第三节中给出了块左循环算子矩阵的范数估计.第四章总结了本文的主要工作,并给出了相关内容的一些建议和展望.
[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，

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