Hankel算子的乘积与有限秩算子

李永宁, 丁宣浩

数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 493-500.

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PDF(446 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 493-500. DOI: 10.12386/A2021sxxb0043
论文

Hankel算子的乘积与有限秩算子

    李永宁1,2, 丁宣浩1,2
作者信息 +

The Product of Hankel Operators and the Finite Rank Operators

    Yong Ning LI1,2, Xuan Hao DING1,2
Author information +
文章历史 +

摘要

f,g,u ∈ ∩q>1 HqHfHgHu均为通常的单位圆盘上的Hardy空间H2H2上的Hankel算子.本文完全刻画了Hardy空间上的三个Hankel算子的乘积HfHgHu是有限秩的充要条件,并给出了两个不平凡的例子.而且,我们利用本文的主要结果刻画了模型空间上有限秩的截断Toeplitz算子.

Abstract

Suppose f, g, u ∈ ∩q>1 Hq, Hf, Hg, Hu are Hankel operators from the usual Hardy space of unit disk H2 to H2. In this paper, we completely characterize when the product of three Hankel operators i>HfHgHu on Hardy space has finite rank property, and we also give two nontrivial examples. Moreover, we describe the finite rank property of truncated Toeplitz operators defined on the model space.

关键词

Hardy空间 / Hankel算子 / 截断Toeplitz算子

Key words

Hardy spaces / Hankel operators / truncated Toeplitz operators

引用本文

导出引用
李永宁, 丁宣浩. Hankel算子的乘积与有限秩算子. 数学学报, 2021, 64(3): 493-500 https://doi.org/10.12386/A2021sxxb0043
Yong Ning LI, Xuan Hao DING. The Product of Hankel Operators and the Finite Rank Operators. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 493-500 https://doi.org/10.12386/A2021sxxb0043

参考文献

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基金

国家自然科学基金资助项目(11871122);重庆市自然科学基金(cstc2018jcyjAX0595,cstc2020jcyj-msxmX0318);重庆工商大学基金(2053010)

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