On the B-discrete spectrum

Abstract

In this paper, we introduce the B-discrete spectrum of an unbounded closed operator and we prove that a closed operator has a purely B-discrete spectrum if and only if it has a meromorphic resolvent. After that, we study the stability of the B-discrete spectrum under several type of perturbations and we establish that two closed invertible linear operators having quasisimilar totally paranormal inverses have equal spectra and B-discrete spectra.