Complementation and Lebesgue-type decompositions of linear operators and relations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-15 DOI:10.1112/jlms.12900

S. Hassi, H. S. V. de Snoo

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引用次数: 0

Abstract

In this paper, a new general approach is developed to construct and study Lebesgue-type decompositions of linear operators or relations $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue-type decompositions than what has been studied in the literature so far. The key point is that it allows a nontrivial interaction between the closable and the singular components of $T$ . The motivation to study such decompositions comes from the fact that they naturally occur in the corresponding Lebesgue-type decomposition for pairs of quadratic forms. The approach built in this paper uses so-called complementation in Hilbert spaces, a notion going back to de Branges and Rovnyak.

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线性算子和关系的补全与勒贝格型分解

本文提出了一种新的通用方法，用于构建和研究希尔伯特空间环境中线性算子或关系 T $T$ 的 Lebesgue 型分解。与迄今为止的文献研究相比，新方法可以引入更广泛的 Lebesgue 型分解。关键在于它允许 T $T$ 的可闭成分和奇异成分之间存在非对称的相互作用。研究这种分解的动机来自这样一个事实，即它们自然出现在二次型对的相应 Lebesgue 型分解中。本文建立的方法使用了所谓的希尔伯特空间互补，这一概念可追溯到 de Branges 和 Rovnyak。

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

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.