Extended Rakočević's property

2020/07/22 by Ouidren, kaoutar Ben, Zariouh, Hassan
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2007.11710

Abstract

The purpose of this paper is to introduce and study new extension of Rakočević's property (w) and property (b) introduced by Berkani--Zariouh in \citeberkani-zariouh1, in connection with other Weyl type theorems and recent properties. We prove in particular, the two following results: 1. A bounded linear operator T satisfies property (w_π₀₀) if and only if T satisfies property (w) and σ_uf(T)=σ_uw(T). 2. T satisfies property (gw_π₀₀) if and only if T satisfies property (w_π₀₀) and π₀(T)=p₀^a(T). Classes of operators are considered as illustrating examples.

Related

• On the property (Z_Ea)
• Properties (BR) and (BgR) for Bounded Linear Operators
• Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators
• Extension properties for monotone and sublinear operators
• Banach spaces with Property (w)