Toeplitz operators with monomial symbols on the Dirichlet spaces

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-04-17 DOI:10.1007/s43034-024-00346-9

Sumin Kim, Jongrak Lee

引用次数: 0

Abstract

In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators \(T_{\varphi }\) with monomial symbols \(\varphi \). Third, we give a necessary and sufficient conditions for the normality and hyponormality of the Toeplitz operators \(T_{\varphi }\) with such symbols on the Dirichlet spaces.

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狄利克空间上具有单项式符号的托普利兹算子

在本文中，我们关注的是作用于 Dirichlet 空间的托普利兹算子的各种性质。首先，我们考虑带谐波符号和单项式符号的托普利兹算子的矩阵表示。其次，我们建立了具有单项式符号 \(\varphi \) 的托普利兹算子 \(T_{\varphi }\) 的扩张性和收缩性。第三，我们给出了具有此类符号的托普利兹算子 \(T_{\varphi }\) 在德里赫利特空间上的正态性和次正态性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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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.