Composition operators with closed range on the Dirichlet space

IF 1.1 2区数学 Q1 MATHEMATICS

Banach Journal of Mathematical Analysis Pub Date : 2024-03-30 DOI:10.1007/s43037-024-00334-0

Guangfu Cao, Li He

引用次数: 0

Abstract

It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Nevanlinna counting function induces a reverse Carleson measure. Similar conclusion is not available on the Dirichlet space. Specifically, the reverse Carleson measure is not enough to ensure that the range of the corresponding composition operator is closed. However, under certain assumptions, we in this paper set the necessary and sufficient condition for a composition operator on the Dirichlet space to have closed range.

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迪里希勒空间上具有封闭范围的合成算子

众所周知，哈代或伯格曼空间上的组成算子有一个封闭的范围，当且仅当其内万林纳计数函数诱导一个反向卡列松度量时。类似的结论在 Dirichlet 空间上并不存在。具体地说，反向卡列松度量不足以确保相应组成算子的范围是封闭的。然而，在某些假设条件下，我们在本文中设定了迪里希勒空间上的组成算子具有封闭范围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

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. 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 operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.