A BOUND for SIMILARITY CONDITION NUMBERS of UNBOUNDED OPERATORS with HILBERT-SCHMIDT HERMITIAN COMPONENTS

Michael Gil'

doi:10.1017/S1446788714000354

A BOUND for SIMILARITY CONDITION NUMBERS of UNBOUNDED OPERATORS with HILBERT-SCHMIDT HERMITIAN COMPONENTS

Michael Gil'

Department of Mathematics

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

7 Scopus citations

Abstract

Let H be a linear unbounded operator in a Hilbert space. It is assumed that the resolvent of H is a compact operator and H - H is a Hilbert-Schmidt operator. Various integro-differential operators satisfy these conditions. It is shown that H is similar to a normal operator and a sharp bound for the condition number is suggested. We also discuss applications of that bound to spectrum perturbations and operator functions.

Original language	English
Pages (from-to)	331-342
Number of pages	12
Journal	Journal of the Australian Mathematical Society
Volume	97
Issue number	3
DOIs	https://doi.org/10.1017/S1446788714000354
State	Published - 20 Jun 2014

Keywords

condition numbers
norm of operator function
operators
similarity
spectrum perturbations

ASJC Scopus subject areas

General Mathematics

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10.1017/S1446788714000354

Cite this

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abstract = "Let H be a linear unbounded operator in a Hilbert space. It is assumed that the resolvent of H is a compact operator and H - H is a Hilbert-Schmidt operator. Various integro-differential operators satisfy these conditions. It is shown that H is similar to a normal operator and a sharp bound for the condition number is suggested. We also discuss applications of that bound to spectrum perturbations and operator functions.",

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AB - Let H be a linear unbounded operator in a Hilbert space. It is assumed that the resolvent of H is a compact operator and H - H is a Hilbert-Schmidt operator. Various integro-differential operators satisfy these conditions. It is shown that H is similar to a normal operator and a sharp bound for the condition number is suggested. We also discuss applications of that bound to spectrum perturbations and operator functions.

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KW - norm of operator function

KW - operators

KW - similarity

KW - spectrum perturbations

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A BOUND for SIMILARITY CONDITION NUMBERS of UNBOUNDED OPERATORS with HILBERT-SCHMIDT HERMITIAN COMPONENTS

Abstract

Keywords

ASJC Scopus subject areas

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