Operators which have a closed quasi-nilpotent part

By P. Aiena, M. Colasante, Manuel González. 2002

72 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Classes of operators satisfying a-Weyl's theorem (2005, background): “We shall consider a local version of this property, which has been studied in recent papers [3], [4], [6], and previously by Finch [20] and Mbekhta [29].”
On Drazin invertibility (2008, background): “The implications (1), (2), (3) and (4) are actually equivalences if T is a semi-Fredholm operator; see [5] or [1, Chapter 3].”
Single-valued extension property at the points of the approximate point spectrum (2003, background): “The SVEP at a point λo has been characterized in several ways in the case that λoI − T is of Kato type, see [2,3,5].”
Variations on Weyl's theorem (2006, background): “We also have H0(λI − T ) closed ⇒ T has SVEP at λ, (5) and also this implication is actually an equivalence if λI − T ∈Φ±(X), see [5].”
Weyl's and Browder's theorems for operators satisfying the SVEP (2004, background): “In [1] (see also [16]), it was shown that if for an operator T ∈ L(X), H0(T − λ) is closed for every complex number λ, then T has the SVEP.”
Property (w) for perturbations of polaroid operators (2008, unknown): “Note that, (see [4]), H0(λI − T ) closed ⇒ T has SVEP at λ, (7) and this implication is an equivalence whenever λI − T ∈ ±(X), see [4].”