Numerical ranges of cube roots of the identity

被引：5

作者：

Harris, Thomas Ryan ^{[1
]}

Mazzella, Michael ^{[1
]}

Patton, Linda J. ^{[1
]}

Renfrew, David ^{[1
]}

Spitkovsky, Ilya M.

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 11期

关键词：

Numerical range; Algebraic operator; Threefold symmetry; 3X3; MATRICES; OPERATORS;

D O I：

10.1016/j.laa.2011.03.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical range of a bounded linear operator T on a Hilbert space His defined to be the subset W(T) = {< Tv, v >: v is an element of H, parallel to v parallel to = 1} of the complex plane. For operators on a finite-dimensional Hilbert space, it is known that if W(T) is a circular disk then the center of the disk must be a multiple eigenvalue of T. In particular, if T has minimal polynomial z(3) - 1, then W(T) cannot be a circular disk. In this paper we show that this is no longer the case when H is infinite dimensional. The collection of 3 x 3 matrices with threefold symmetry about the origin are also classified. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2639 / 2657

页数：19

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