Hardy空间上的Davis-Wielandt壳和复合算子的数值范围

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-10-20 DOI:10.1007/s43034-025-00468-8

Xiaolu Liu, Liu Liu

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引用次数: 0

摘要

本文研究了Hardy空间上的Davis-Wielandt壳和复合算子的数值范围。首先，我们给出了带有矩阵符号的乘法算子的Davis-Wielandt壳的一个表征。随后，我们刻画了由常数函数、定0内函数和2阶椭圆自同构诱导的复合算子的Davis-Wielandt壳。进一步，我们分析了由抛物自同构和椭圆自同构诱导的复合算子的Davis-Wielandt壳的对称性。此外，我们还完整地描述了由3阶椭圆自同构诱导的复合算子的数值范围。

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The Davis-Wielandt shell and the numerical range of composition operators on the Hardy space

In this paper, we investigate the Davis-Wielandt shell and the numerical range of composition operators on the Hardy space. Firstly, we give a characterization of the Davis-Wielandt shell for multiplication operators with matrix symbols. Subsequently, we characterize the Davis-Wielandt shell of composition operators induced by constant functions, inner functions fixing 0 and elliptic automorphisms of order 2. Furthermore, we analyze the symmetry of the Davis-Wielandt shell for composition operators induced by parabolic automorphisms or elliptic automorphisms. Additionally, we present a complete description of the numerical range for composition operators induced by elliptic automorphisms of order 3.

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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.