6533b836fe1ef96bd12a082e

RESEARCH PRODUCT

Operators which have a closed quasi-nilpotent part

Manuel GonzálezPietro AienaMaria Luisa Colasante

subject

Unbounded operatorDiscrete mathematicsPure mathematicsApproximation propertyApplied MathematicsGeneral MathematicsSpectrum (functional analysis)Finite-rank operatorSpectral theoremOperator theoryOperator normFourier integral operatorMathematics

description

We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.

yearjournalcountryeditionlanguage
2002-03-12Proceedings of the American Mathematical Society
https://doi.org/10.1090/s0002-9939-02-06386-4