Some characterizations of minimal matrices with operator norm

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-11-05 DOI:10.1007/s43034-024-00393-2

Shuaijie Wang, Ying Zhang

引用次数: 0

Abstract

This paper studies matrices A in $M_n(\mathbb C)$ satisfying

$$\begin{aligned} \Vert A\Vert =\min \{\Vert A+B\Vert :B\in {\mathcal {B}}\}, \end{aligned}$$

where ${\mathcal {B}}$ is a C*-subalgebra of $M_n(\mathbb C)$ and $\Vert \cdot \Vert $ denotes the operator norm. Such an A is called ${\mathcal {B}}$-minimal. The necessary and sufficient conditions for A to be ${\mathcal {B}}$-minimal are characterized, and a constructive method to obtain ${\mathcal {B}}$-minimal normal matrices is provided. Moreover, $\bigoplus _{i=1}^k{\mathcal {B}}$-minimal normal matrices with anti-diagonal block form are studied.

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具有算子规范的最小矩阵的一些特征

本文研究的是$M_n(\mathbb C)$中满足$$\begin{aligned}的矩阵A。\Vert A\Vert =min \{Vert A+B\Vert :B\in {\mathcal {B}}\}, \end{aligned}$$其中 ${\mathcal {B}}$ 是 $M_n(\mathbb C)$的 C* 子代数，并且 $\Vert \cdot \Vert $表示算子规范。这样的 A 被称为 ${mathcal {B}}$-minimal 。本文描述了 A 是 ${\mathcal {B}}$-minimal 的必要条件和充分条件，并提供了一种得到 ${\mathcal {B}}$-minimal 正矩阵的构造方法。此外，还研究了具有反对角块形式的（\bigoplus _{i=1}^k{\mathcal {B}}）-最小法矩阵。

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

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.