Operators which have a closed quasi-nilpotent part

Aiena, Pietro; Colasante, Maria; González, Manuel

doi:10.1090/S0002-9939-02-06386-4

Operators which have a closed quasi-nilpotent part
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by Pietro Aiena, Maria Luisa Colasante and Manuel González PDF

Proc. Amer. Math. Soc. 130 (2002), 2701-2710 Request permission

Abstract:

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.

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