Open AccessOn the stability of the localized single-valued extension property under commuting perturbations
Author(s) -
Pietro Aiena,
Michael Neumann
Publication year - 2013
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/s0002-9939-2013-11635-7
Subject(s) - extension (predicate logic) , property (philosophy) , nilpotent , mathematics , algebraic number , pure mathematics , single point , stability (learning theory) , point (geometry) , algebra over a field , mathematical analysis , geometry , computer science , philosophy , epistemology , limit (mathematics) , machine learning , programming language
This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators