哈代空间上托普利兹算子或汉克尔算子的偏斜换向器

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-06 DOI:10.1007/s43037-024-00330-4

Yongning Li, Hanyi Zheng, Xuanhao Ding

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引用次数: 0

摘要

设 A 和 B 是希尔伯特空间上的两个有界线性算子。如果 \(_{*}[A,B]=AB-BA^{*}=0.\)，则 B 称为 A 的偏斜换元子。在本文中，我们完全描述了哈代空间上的托普利兹算子何时是汉克尔算子的偏斜换元子，以及哈代空间上的汉克尔算子何时是托普利兹算子的偏斜换元子。此外，我们还得到了汉克尔算子和托普利兹算子的乘积在哈代空间上自相交的必要条件和充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces

Let A and B be two bounded linear operators on a Hilbert space. B is called the skew commutator of A if \(_{*}[A, B]=AB-BA^{*}=0.\) In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient condition for the product of a Hankel operator and a Toeplitz operator to be self-adjoint on the Hardy space.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.