Inner bounds for the spectrum of quasinormal operators

M. I. Gil

doi:10.1090/S0002-9939-03-06950-8

Inner bounds for the spectrum of quasinormal operators

M. I. Gil

Department of Mathematics

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

3 Scopus citations

Abstract

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

Original language	English
Pages (from-to)	3737-3746
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9939-03-06950-8
State	Published - 1 Dec 2003

Keywords

Finite and infinite matrices
Integral operators
Linear operators
Spectral radius
Spectrum

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-03-06950-8

Cite this

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AB - A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

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KW - Integral operators

KW - Linear operators

KW - Spectral radius

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Inner bounds for the spectrum of quasinormal operators

Abstract

Keywords

ASJC Scopus subject areas

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