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

Michael Gil'

doi:10.1017/S0004972721000241

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

Michael Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	146-153
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	105
Issue number	1
DOIs	https://doi.org/10.1017/S0004972721000241
State	Published - 16 Feb 2022

Keywords

Differential operator
Hilbert space
Spectrum localisation

ASJC Scopus subject areas

General Mathematics

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10.1017/S0004972721000241

Cite this

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title = "AN UNBOUNDED OPERATOR WITH SPECTRUM IN A STRIP AND MATRIX DIFFERENTIAL OPERATORS",

abstract = "Let A and {\~A} 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 {\~A} lie, if A and {\~A} are sufficiently 'close'? We derive a sharp bound for the strip containing the spectrum of {\~A}, assuming that {\~A} - A is a bounded operator and A has a bounded Hermitian component. We also discuss applications of our results to regular matrix differential operators.",

keywords = "Differential operator, Hilbert space, Spectrum localisation",

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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 - https://www.scopus.com/pages/publications/85104354944

U2 - 10.1017/S0004972721000241

DO - 10.1017/S0004972721000241

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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