Essential Spectra and Drazin Invertibility of Quasisimilar Closed Operators

Received: 26.X.2016, Accepted: 8.III.2017

Abstract. The purpose of this paper is to introduce several generalizations of the notion of similarity between closed operators on a Hilbert space, in particular, the notion of quasi-similarity and mutually quasi-similarity. Furthermore, we explore to what extend they preserve
spectral properties, Drazin invertibility and hyperinvariant subspaces.

Keywords: Similarity, Quasi-similarity, Mutually quasi-similarity, Fredholm spectrums, Drazin invertibility, hyperinvariant subspaces

Mathematics Subject Classification (2010): Primary 47A05, 47B33, 47A10

Authors:
Ghouti Djellouli, University of Saida, Po. Box 138, Saida, Algeria
Abdelhalim Azzouz, University of Saida, Po. Box 138, Saida, Algeria
Bekkai Messirdi, Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO), Algeria