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
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
收藏
页码:2639 / 2657
页数:19
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