投影对的广义铅笔的特征

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-12 DOI:10.1007/s43037-023-00322-w

Tao Chen, Weining Lai, Chunyuan Deng

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引用次数: 0

摘要

让 T 成为复希尔伯特空间（\mathcal {H}\）上的有界线性算子。我们提出了一些必要条件和充分条件，即 T 是一对（P, Q）在某个点 \((\alpha , \beta )\in \mathbb {C}^2\)上的投影的广义铅笔 \(P+\alpha Q +\beta PQ\) 。研究了广义铅笔 T 的范围和核关系，并对一些特殊广义铅笔的附加性质给出了评论。

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Characterizations of generalized pencils of pairs of projections

Let T be a bounded linear operator on a complex Hilbert space \(\mathcal {H}\). We present some necessary and sufficient conditions for T to be the generalized pencil \(P + \alpha Q +\beta PQ\) of a pair (P, Q) of projections at some point \((\alpha , \beta )\in \mathbb {C}^2\). The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some special generalized pencil are given.

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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.