权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Studies of the structure of operators on analytic function spaces and their invariant subspaces

解析函数空间及其不变子空间算子结构的研究

基本信息

批准号：
16340037
负责人：
IZUCHI Keiji
金额：
$ 6.4万
依托单位：
Niigata University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340037/
关键词：
analytic function space invariant subspace backward shift invariant subspace Hardy space bounded analytic functions composition operator singular inner function commutative Banach algebra トラース公式荷重解析関数空間ハーディ空間バーグマン空間テープリッツ作用素

项目摘要

Izuchi (head of investigator) got the following results as the joint works.1) Let M be an invariant subspace on the Hardy space over the bidisk. We have multiplication operators R_z and R_w on M. It is given a characterization of M for which rank[R_z, R*_w]=1. Also it is determined N=H^2Θ M satisfying rank[S_z, S*_w]=1.2) It is given a lower and upper bound of the essential norms of the difference of composition operators on the space of bounded analytic functions H∞ on the open unit disk D. Also it is studied the topological structure of weighted composition operators on H∞.3) It is studied quasi-invariant subspaces of the Fock space over C-2 generated by a polynomial.4) It is given a characterization of two Hankel operators on H^2 for which their product is a compact perturbation of Hankel operator.5) It is given a partial answer for Gorkin-Mortini' s problem on closed prime ideals of H∞.6) It is studied a common zero set of equivalent singular inner functions in the maximal ideal space of H∞. Also it is solved two problems on singular inner functions posed by Mortini and Nicolau.Nakazi (investigator) studied a commutant lifting theorem for compression operators.Ohno (investigator) studied compact Hankel-type operators on the space of bounded harmonic functions h∞ on D. Also it is determined the essential norms of difference of composition operators on H∞.

Izuchi（研究小组组长）在联合工作中得到了以下结果：1）设M是双圆盘上哈代空间上的不变子空间。我们有M上的乘法算子R_z和R_w。给出了秩[R_z，R*_w]=1的M的一个特征. 2）给出了开单位圆盘D上有界解析函数空间H∞上复合算子差的本质范数的一个上、下界。研究了H∞上加权复合算子的拓扑结构; 3）研究了C-2上Fock空间中由多项式生成的拟不变子空间; 4）给出了H ^2上两个Hankel算子的一个特征，使得它们的乘积是Hankel算子的紧扰动; 5）给出了H∞闭素理想上Gorkin-Mortini问题的部分解答; 6）研究了H∞的极大理想空间中等价奇异内函数的公共零点集。Nakazi（研究者）研究了压缩算子的交换提升定理，Ohno（研究者）研究了D上有界调和函数空间h∞上的紧Hankel型算子.并确定了H∞上复合算子的差分的本质范数。