ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS

被引：0

作者：

Bernik, J. ^{[1
]}

Livshits, L. ^{[2
]}

MacDonald, G. ^{[3
]}

Marcoux, L. ^{[4
]}

Mastnak, M. ^{[5
]}

Radjavi, H. ^{[4
]}

机构：

[1] Univ Ljubljani, Fak Matematiko Fiziko, Jadranska 19, Ljubljana 1000, Slovenia

[2] Colby Coll, Dept Math, Waterville, ME 04901 USA

[3] Univ Prince Edward Isl, Sch Math & Computat Sci, Charlottetown, PE C1A 4P3, Canada

[4] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[5] St Marys Univ, Dept Math & Comp Sci, 923 Robie ST, Halifax, NS B3N 1Z9, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 10期

关键词：

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

D O I：

10.1090/proc/15523

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-lambda I) <= m - 2 for some lambda is an element of C.

引用

页码：4083 / 4097

页数：15

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