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Researches on Properties of the Spaces of Analytic Functions and Their Operators

解析函数及其算子空间性质的研究

基本信息

批准号：
15540181
负责人：
OHNO Shuichi
金额：
$ 1.28万
依托单位：
Nippon Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540181/
关键词：
Hardy spaces Bloch spaces bounded harmonic functions composition operators Toeplitz operators weighted composition operators boundedness compactness Bergman空間 Hankel-type作用素 compactness Hard空間関数環

项目摘要

(1) S. Ohno, K. Stroethoff and R. Zhao characterized the necessary and sufficient conditions for weighted composition operators to be bounded or compact between Bloch-type spaces of analytic functions on the unit disk including Lipschitz spaces and Bloch spaces. We published a paper. (2) J. S. Choa and S. Ohno investigated the boundedness and compactness of the products of composition and analytic Toepliz Operators. Originally this form is found in the question posed by Deddens and Wong which is concerned with the existence of an analytic Toeplitz operator commuting with a non-zero compact operator. We obtained the results on Hardy and Bergman spaces. This result was published. (3) T. Hosokawa, K. Izuchi and S. Ohno studied properties of the topological space of weighted composition operators on the space of bounded analytic functions on the open unit disk in the uniform operator topology. Moreover, we characterized the compactness of the differences of two weighted composition operators. The paper was accepted and so will be appeared (4) K. Izuchi and S. Ohno investigated Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras. The paper was accepted and so will be appeared. (5) T. Hosokawa and S. Ohno studied the boundedness and the compactness of the differences of two composition operators on the Bloch and the little Bloch spaces. We proved that the weak compactness of the differences on the little Bloch space is equivalent to the compactness. Moreover we gave attention to the topological structure of the space of composition operators on the Bloch space in the operator topology.

(1)S.Ohno，K.Stroethoff和R.赵刻画了单位圆盘上解析函数的Bloch型空间(包括Lipschitz空间和Bloch空间)之间加权复合算子有界或紧的充要条件。我们发表了一篇论文。(2)J.S.Choa和S.Ohno研究了复合Toepliz算子和解析Toepliz算子乘积的有界性和紧性。最初，这种形式是在Dedden和Wong提出的问题中找到的，该问题涉及与非零紧算子交换的解析Toeplitz算子的存在性。我们得到了Hardy空间和Bergman空间上的结果。这一结果发表了。(3)T.Hosokawa，K.Izuchi和S.Ohno在一致算子拓扑中研究了开单位圆盘上有界解析函数空间上加权复合算子的拓扑空间的性质。此外，我们还刻画了两个加权复合算子之差的紧性。(4)K.Izuchi和S.Ohno研究了开单位圆盘上有界调和函数空间上的Hankel型算子。这些算子与紧一致代数、Dunford-Pettis性质和Bourain代数有关。这篇论文被接受了，因此将会出现。(5)T.Hosokawa和S.Ohno研究了两个复合算子的差在Bloch空间和小Bloch空间上的有界性和紧性。证明了小Bloch空间上差分的弱紧性与紧性等价。此外，我们还在算子拓扑中考虑了Bloch空间上的复合算子空间的拓扑结构。