Translator Disclaimer
2018 Symmetric numerical ranges of four-by-four matrices
Shelby L. Burnett, Ashley Chandler, Linda J. Patton
Involve 11(5): 803-826 (2018). DOI: 10.2140/involve.2018.11.803

Abstract

Numerical ranges of matrices with rotational symmetry are studied. Some cases in which symmetry of the numerical range implies symmetry of the spectrum are described. A parametrized class of 4×4 matrices K(a) such that the numerical range W(K(a)) has fourfold symmetry about the origin but the generalized numerical range WK(a)(K(a)) does not have this symmetry is included. In 2011, Tsai and Wu showed that the numerical ranges of weighted shift matrices, which have rotational symmetry about the origin, are also symmetric about certain axes. We show that any 4×4 matrix whose numerical range has fourfold symmetry about the origin also has the corresponding axis symmetry. The support function used to prove these results is also used to show that the numerical range of a composition operator on Hardy space with automorphic symbol and minimal polynomial z41 is not a disk.

Citation

Download Citation

Shelby L. Burnett. Ashley Chandler. Linda J. Patton. "Symmetric numerical ranges of four-by-four matrices." Involve 11 (5) 803 - 826, 2018. https://doi.org/10.2140/involve.2018.11.803

Information

Received: 13 December 2016; Revised: 30 July 2017; Accepted: 3 September 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06866585
MathSciNet: MR3784028
Digital Object Identifier: 10.2140/involve.2018.11.803

Subjects:
Primary: 15A60
Secondary: 47B33

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 5 • 2018
MSP
Back to Top