Open AccessOperators with eigenvalues and extreme cases of stability
Author(s) -
Larry Downey,
Per Enflo
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/s0002-9939-03-07059-x
Subject(s) - eigenvalues and eigenvectors , operator (biology) , annotation , perturbation (astronomy) , algorithm , spectrum (functional analysis) , stability (learning theory) , computer science , mathematics , artificial intelligence , chemistry , machine learning , physics , quantum mechanics , biochemistry , repressor , transcription factor , gene
In the following, we consider some cases where the point spectrum of an operator is either very stable or very unstable with respect to small perturbations of the operator. The main result is about the shift operator on l 2 , l_2, whose point spectrum is what we will call strongly stable. We also give some general perturbation results, including a result about the size of the set of operators that have an eigenvalue.