Characterizations of generalized pencils of pairs of projections

IF 1.1 2区数学 Q1 MATHEMATICS Banach Journal of Mathematical Analysis Pub Date : 2024-02-12 DOI:10.1007/s43037-023-00322-w

Tao Chen, Weining Lai, Chunyuan Deng

引用次数: 0

Abstract

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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投影对的广义铅笔的特征

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。

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.

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