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

• 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

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（调查员负责人）得到以下结果。1）让M成为BIDISK上Hardy空间上不变的子空间。我们在M上具有乘法运算符R_Z和R_W。它的表征是rank [r_z，r*_W] = 1的M。此外，它也确定n = h^2θm满足秩[s_z，s*_W] = 1.2）在开放单位磁盘上的组成算子差异的基本规范的下层和上限。 4）在H^2上给出了两个Hankel操作员的特征，其产品是Hankel Operators的紧凑型扰动。5）5）在封闭的Prime Ideas 6）中给出了gorkin-Mortini问题的部分答案。此外，它也解决了Mortini和Nicolau.nakazi（研究人员）提出的两个问题的问题。

项目成果

Products of composition and differentiation between Hardy spaces

• DOI: 10.1017/s0004972700038818
• 发表时间: 2006-04-01
• 期刊: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
• 影响因子: 0.7
• 作者: Ohno, S

Hankel-type operators on the space of bounded Hankel-type operators on the space of bounded harmonic functions.

有界调和函数空间上的 Hankel 型算子 有界 Hankel 型算子。

• 发表时间: 2006
• 期刊: Proc Amer.Math.Soc. 134・5
• 作者: Izuchi;Keiji
• 通讯作者: Keiji

Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products II

Frostman 位移为 Carleson-Newman Blaschke 产品 II 的奇异内部函数

• 期刊: Complex Var. Elliptic Equ. (to appear)
• 作者: Izuchi;Keiji
• 通讯作者: Keiji

Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products

Frostman 平移是 Carleson-Newman Blaschke 产品的奇异内部函数

• 发表时间: 2006
• 期刊: Complex Var. Elliptic Equ. 51・3
• 作者: Izuchi;Keiji
• 通讯作者: Keiji

Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products.

其 Frostman 移位的奇异内部函数是 Carleson-Newman Blaschke 产品。

• 发表时间: 2006
• 期刊: Complex Var.Elliptic Equ. 51・3
• 作者: Izuchi;Keiji
• 通讯作者: Keiji