UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS

Thumbnail Image

Files

BernikJ LivshitsL MacDonaldGW MarcouxLW MastnakM RadjaviH 2020 Algebraic degree in spatial matricial numerical ranges of linear operators.pdf (364.18 KB)

Date

2021-07-20

Authors

Bernik, Janez
Livshits, Leo
MacDonald, Gordon W.
Marcoux, Laurent W.
Mastnak, Mitja
Radjavi, Heydar

Journal Title

Journal ISSN

Volume Title

Publisher

American Mathematical Society

Abstract

We study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L on a Hilbert space, every principal m-dimensional ortho-compression of L has algebraic degree less than m if and only if rank(L − λI) ≤ m − 2 for some λ ∈ C

Description

First published in Proceedings of the American Mathematical Society in volume 149, issue 10 in 2021, published by the American Mathematical Society

Keywords

spatial matricial numerical ranges, algebraic degree, rank modulo scalars, orthogonal compressions, principal submatrices, cyclic matrices, non-derogatory matrices

LC Keywords

Citation

URI

https://doi.org/10.1090/proc/15523
 http://hdl.handle.net/10012/18251

Collections

Waterloo Research
Pure Mathematics