scispace - formally typeset
Search or ask a question
Author

Bekkai Messirdi

Other affiliations: École Normale Supérieure
Bio: Bekkai Messirdi is an academic researcher from University of Oran. The author has contributed to research in topics: Operator theory & Invertible matrix. The author has an hindex of 6, co-authored 40 publications receiving 123 citations. Previous affiliations of Bekkai Messirdi include École Normale Supérieure.

Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the authors studied the left and right generalized Drazin inverse of bounded operators in a Banach space and showed that these sets are compact in the complex plane and invariant under additive commuting quasi-nilpotent perturbations.
Abstract: In this paper, we define and study the left and the right generalized Drazin inverse of bounded operators in a Banach space We show that the left (resp the right) generalized Drazin inverse is a sum of a left invertible (resp a right invertible) operator and a quasi-nilpotent one In particular, we define the left and the right generalized Drazin spectra of a bounded operator and also show that these sets are compact in the complex plane and invariant under additive commuting quasi-nilpotent perturbations Furthermore, we prove that a bounded operator is left generalized Drazin invertible if and only if its adjoint is right generalized Drazin invertible An equivalent definition of the pseudo-Fredholm operators in terms of the left generalized Drazin invertible operators is also given Our obtained results are used to investigate some relationships between the left and right generalized Drazin spectra and other spectra founded in Fredholm theory

22 citations

01 Jan 2014
TL;DR: In this paper, the essentially semi-regular spectrum of closed, densely defined linear operator is stable under commuting compact perturbation and its Kato spectrum is stable subjected to additive commuting nilpotent perturbations.
Abstract: In this paper, we give some proprieties of the semi-regular, essentially semi-regular and the operators of Kato type on a Banach space We also show that the essentially semi-regular spectrum of closed, densely defined linear operator is stable under commuting compact perturbation and its Kato spectrum is stable subjected to additive commuting nilpotent perturbations

12 citations

Posted Content
TL;DR: In this paper, the authors give characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP).
Abstract: In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if and only if admits a generalized Kato decomposition and has the SVEP at 0 (resp. it admits a generalized Kato decomposition and its adjoint has the SVEP at 0. In addition, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting finite rank perturbations. Furthermore, we investigate the transmission of some local spectral properties from a bounded linear operator, as the SVEP, Dunford property $(C)$, and property $(\beta)$, to its generalized Drazin inverse.

9 citations

Journal Article
TL;DR: In this article, the spectral analysis of the pair (A,B) of bounded linear operators acting on two complex Banach spaces with value on a complex number is studied, and the functional calculus for the pair is used to prove the corresponding spectral mapping theorem.
Abstract: Let X and Y two complex Banach spaces and (A,B) a pair of bounded linear operators acting on X with value on Y. This paper is concerned with spectral analysis ofthe pair (A;B): We establish some properties concerning the spectrum of the linear operator pencils (A-lambda B) when B is not necessarily invertible and lambda is a complex number. Also, we use the functional calculus for the pair (A,B) to prove the corresponding spectral mapping theorem for (A,B). In addition, we de fi ne the generalized Kato essential spectrum and the closed range spectra of the pair (A,B) and we give some relationships between this spectrums. As application, we describe a spectral analysis of quotient operators.

7 citations


Cited by
More filters
01 Jan 2016
TL;DR: The methods of modern mathematical physics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.

1,536 citations

Book ChapterDOI
31 Dec 1927

111 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived the spectral shift function of the operator DA and derived the Fredholm index of DA with respect to the spectral flow SpFlow, which coincides with a spectral flow for the pair (A+A−A−) of asymptotic operators.

50 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that left and right (b, c ) -invertibility of a semigroup together imply (b, c )-invertability.

35 citations