Boundedness, compactness and Schatten class for Rhaly matrices

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-29 DOI:10.1112/jlms.70304

Carlo Bellavita, Eugenio Dellepiane, Georgios Stylogiannis

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引用次数: 0

Abstract

In this article we present new proofs for the boundedness and the compactness on $ℓ^{2}$ of the Rhaly matrices, also known as terraced matrices. We completely characterize when such matrices belong to the Schatten class $S^{q} (ℓ^{2})$ , for $1 < q < \infty$ . Finally, we apply our results to study the Hadamard multipliers in weighted Dirichlet spaces, answering a question left open by Mashreghi–Ransford.

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Rhaly矩阵的有界性、紧性和Schatten类

在本文中，我们给出了列矩阵在l2 $\ell ^2$上的有界性和紧性的新证明。我们完全刻画了这些矩阵何时属于Schatten类sq (l2) $\mathcal {S}^q(\ell ^2)$，对于1 ＆lt； q ＆lt;∞$1<q<\infty$。最后，我们应用我们的结果研究了加权Dirichlet空间中的Hadamard乘数，回答了Mashreghi-Ransford遗留的一个问题。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.