TY - JOUR

T1 - AN UNBOUNDED OPERATOR WITH SPECTRUM IN A STRIP AND MATRIX DIFFERENTIAL OPERATORS

AU - Gil', Michael

N1 - Publisher Copyright:
© 2021 Australian Mathematical Publishing Association Inc.

PY - 2022/2/16

Y1 - 2022/2/16

N2 - Let A and Ã be unbounded linear operators on a Hilbert space. We consider the following problem. Let the spectrum of A lie in some horizontal strip. In which strip does the spectrum of Ã lie, if A and Ã are sufficiently 'close'? We derive a sharp bound for the strip containing the spectrum of Ã, assuming that Ã - A is a bounded operator and A has a bounded Hermitian component. We also discuss applications of our results to regular matrix differential operators.

AB - Let A and Ã be unbounded linear operators on a Hilbert space. We consider the following problem. Let the spectrum of A lie in some horizontal strip. In which strip does the spectrum of Ã lie, if A and Ã are sufficiently 'close'? We derive a sharp bound for the strip containing the spectrum of Ã, assuming that Ã - A is a bounded operator and A has a bounded Hermitian component. We also discuss applications of our results to regular matrix differential operators.

KW - Differential operator

KW - Hilbert space

KW - Spectrum localisation

UR - http://www.scopus.com/inward/record.url?scp=85104354944&partnerID=8YFLogxK

U2 - 10.1017/S0004972721000241

DO - 10.1017/S0004972721000241

M3 - Article

AN - SCOPUS:85104354944

SN - 0004-9727

VL - 105

SP - 146

EP - 153

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 1

ER -