Inverse continuity of the numerical range map for hilbert space operators

Brian Lins; Ilya M. Spitkovsky

doi:10.7153/oam-2020-14-06

Inverse continuity of the numerical range map for hilbert space operators

Brian Lins, Ilya M. Spitkovsky

Mathematics

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

Abstract

We describe continuity properties of the multivalued inverse of the numerical range map f_A: x →(Ax,x) associated with a linear operator A defined on a complex Hilbert space H. We prove in particular that f^-1 _A is strongly continuous at all points of the interior of the numerical range W(A). We give examples where strong and weak continuity fail on the boundary and address special cases such as normal and compact operators.

Original language	English (US)
Article number	OaM-14-06
Pages (from-to)	77-90
Number of pages	14
Journal	Operators and Matrices
Volume	14
Issue number	1
DOIs	https://doi.org/10.7153/oam-2020-14-06
State	Published - Mar 2020

Keywords

Inverse continuity
Numerical range
Weak continuity

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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abstract = "We describe continuity properties of the multivalued inverse of the numerical range map fA: x →(Ax,x) associated with a linear operator A defined on a complex Hilbert space H. We prove in particular that f-1 A is strongly continuous at all points of the interior of the numerical range W(A). We give examples where strong and weak continuity fail on the boundary and address special cases such as normal and compact operators.",

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AB - We describe continuity properties of the multivalued inverse of the numerical range map fA: x →(Ax,x) associated with a linear operator A defined on a complex Hilbert space H. We prove in particular that f-1 A is strongly continuous at all points of the interior of the numerical range W(A). We give examples where strong and weak continuity fail on the boundary and address special cases such as normal and compact operators.

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KW - Weak continuity

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Inverse continuity of the numerical range map for hilbert space operators

Abstract

Keywords

ASJC Scopus subject areas

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