The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices

被引：1

作者：

Itza-Ortiz, Benjamin A. ^{[1
]}

Martinez-Avendano, Ruben A. ^{[2
]}

Nakazato, Hiroshi ^{[3
]}

机构：

[1] Univ Autonoma Estado Hidalgo, Ctr Invest Matemat, Pachuca, Hidalgo, Mexico

[2] Inst Tecnol Autonomo Mexico, Dept Acad Matemat, Mexico City, DF, Mexico

[3] Hirosaki Univ, Dept Math & Phys, Hirosaki, Aomori, Japan

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 15期

关键词：

Numerical range; tridiagonal operators; SPECTRUM;

D O I：

10.1080/03081087.2021.1957760

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove a conjecture stated by the first two authors establishing the closure of the numerical range of a certain class of n + 1-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal (n + 1) x (n + 1) matrices. Furthermore, when n + 1 is odd, we show that the size of such matrices simplifies to n/2 + 1.

引用

页码：2830 / 2849

页数：20

共 38 条

[1] On the numerical ranges of some tridiagonal matrices
Chien, Ruey Ting
Spitkovsky, Ilya M.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 470 : 228 - 240
[2] The numerical range of a class of periodic tridiagonal operators
Itza-Ortiz, Benjamin A.
Martinez-Avendano, Ruben A.
LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (05) : 786 - 806
[3] The numerical range of a periodic tridiagonal operator reduces to the numerical range of a finite matrix
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Martinez-Avendano, Ruben A.
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[4] LINE SEGMENTS ON THE BOUNDARY OF THE NUMERICAL RANGES OF SOME TRIDIAGONAL MATRICES
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[8] NUMERICAL RANGES OF SOME FOGUEL OPERATORS
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[9] Numerical range and numerical radius for some operators
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[10] Numerical ranges of weighted shift matrices with periodic weights
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