Open AccessInner bounds for the spectrum of quasinormal operators
Author(s) -
Michael Gil
Publication year - 2003
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-03-06950-8
Subject(s) - mathematics , hilbert space , spectrum (functional analysis) , operator (biology) , spectral radius , separable space , radius , linear operators , operator theory , operator matrix , quasinormal operator , pure mathematics , compact operator , nuclear operator , mathematical analysis , finite rank operator , eigenvalues and eigenvectors , physics , banach space , computer science , quantum mechanics , extension (predicate logic) , biochemistry , chemistry , computer security , repressor , transcription factor , bounded function , gene , programming language
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.