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On the definition of pseudospectra
Author(s) -
Shargorodsky E.
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp031
Subject(s) - mathematics , bounded function , inequality , operator (biology) , pure mathematics , linear operators , bounded operator , mathematical economics , calculus (dental) , algebra over a field , mathematical analysis , medicine , biochemistry , chemistry , dentistry , repressor , transcription factor , gene
It is well known that the ε‐pseudospectrum of a bounded linear operator defined with the help of a strict inequality is equal to the union of the spectra of all perturbed operators with perturbations that have norms strictly less than ε. The aim of the paper is to show that the same is not true in the case of non‐strict inequalities.