Properties (BR) and (BgR) for Bounded Linear Operators

2018/11/22 by Gupta, Anuradha, Kumar, Ankit
#47A11 #47A55 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A10 #Secondary 47A53 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1811.09184

Abstract

In this paper we introduce the notion of property (BR) and property (BgR) for bounded linear operators defined on an infinite-dimensional Banach space. These properties in connection with Weyl type theorems and in the frame of polaroid operators are investigated. Moreover, we study the stability of these properties under perturbations by commuting finite-dimensional, quasi-nilpotent, Riesz and algebraic operators.

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