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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta Feb. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-01-0015 

Artículos

Furter common local spectral properties for bounded linear operators

1 Sidi Mohamed Ben Abdellah University, Dept. of Mathematics, Fez, Morocco. E-mail: hassane.zguitti@usmba.ac.ma

Abstract

We study common local spectral properties for bounded linear operators A ∈ ℒ(X,Y)

and B,C ∈ ℒ (Y,X) such that

A(BA) 2 =ABACA=ACABA=(AC) 2 A.

We prove that AC and BA share the single valued extension property, the Bishop property (β), the property (β ε ), the decomposition property (δ) and decomposability. Closedness of analytic core and quasinilpotent part are also investigated. Some applications to Fredholm operators are given.

Keywords: Jacobson's lemma; Common properties; Local spectral theory.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

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Received: March 2019; Accepted: April 2019

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