加权位移算子的凸循环和不交圆盘循环性质的研究
发布时间：2018-10-15 08:32
【摘要】：本文主要讨论了线性算子动力系统,并给出了若干结果.其研究内容主要涉及四个方面:其一,我们研究了在实或复的标量域上可分Hilbert空间上子空间圆盘循环算子,给出了圆盘循环算子投影,核等重要性质.此外,我们举出一个例子说明了M-圆盘循环不一定能推出M-圆盘传递.我们还给出了子空间-supercyclic半群的性质以及判定子空间-supercyclic半群的两个标准.其二,介绍了如何去判定一个算子是super凸循环的.尤其给出了 Super凸循环标准.另外,我们也研究了(可逆的)双边加权位移算子的凸循环和super凸循环性质.其三,我们介绍了一个新的定义不交圆盘循环.更具体地,我们给出不交圆盘blow-up/collapse性质和不交圆盘循环标准.此外,我们还研究了双边以及单边加权位移算子的不交圆盘循环性质.最后,我们研究了从全纯函数映射到Taylor展式的部分和的不交supercyclic算子.特别地,我们证明出Taylor-type算子组的不交超循环性质等价于不交su-percyclicity. 另外,我们给出一个判定 Taylor-type 算子组的不交 supercyclic 性质的充分条件.
[Abstract]:In this paper, the linear operator dynamical system is discussed, and some results are given. The main contents of this paper are as follows: first, we study the subspace circular disk operators on the scalar domain of real or complex Hilbert, and give some important properties such as the projection and kernel of the circular disk operators. In addition, we give an example to show that the M-disk cycle does not necessarily produce the M-disk transfer. We also give the properties of subspace--supercyclic Semigroups and two criteria for judging subspace--supercyclic Semigroups. Secondly, how to determine that an operator is a super convex loop is introduced. In particular, the Super convex cycle standard is given. In addition, we also study the convex cycle and super convexity of the (reversible) bilateral weighted displacement operator. Thirdly, we introduce a new definition of disjoint disk cycle. More specifically, we give the blow-up/collapse property of disjoint disk and the circular standard of disjoint disk. In addition, we also study the disjoint circular properties of bilateral and unilateral weighted displacement operators. Finally, we study the disjoint supercyclic operators of partial sum mapping from Holomorphic functions to Taylor expansions. In particular, we prove that the disjoint hypercyclic property of Taylor-type operator system is equivalent to disjoint su-percyclicity.. In addition, we give a sufficient condition to judge the disjoint supercyclic property of Taylor-type operator system.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O177
本文编号：2271964
[Abstract]:In this paper, the linear operator dynamical system is discussed, and some results are given. The main contents of this paper are as follows: first, we study the subspace circular disk operators on the scalar domain of real or complex Hilbert, and give some important properties such as the projection and kernel of the circular disk operators. In addition, we give an example to show that the M-disk cycle does not necessarily produce the M-disk transfer. We also give the properties of subspace--supercyclic Semigroups and two criteria for judging subspace--supercyclic Semigroups. Secondly, how to determine that an operator is a super convex loop is introduced. In particular, the Super convex cycle standard is given. In addition, we also study the convex cycle and super convexity of the (reversible) bilateral weighted displacement operator. Thirdly, we introduce a new definition of disjoint disk cycle. More specifically, we give the blow-up/collapse property of disjoint disk and the circular standard of disjoint disk. In addition, we also study the disjoint circular properties of bilateral and unilateral weighted displacement operators. Finally, we study the disjoint supercyclic operators of partial sum mapping from Holomorphic functions to Taylor expansions. In particular, we prove that the disjoint hypercyclic property of Taylor-type operator system is equivalent to disjoint su-percyclicity.. In addition, we give a sufficient condition to judge the disjoint supercyclic property of Taylor-type operator system.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O177
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