Generalized Drazin inverse of restrictions of bounded linear operators

Mohamed Boumazgour

doi:10.1080/03081087.2017.1330867

Generalized Drazin inverse of restrictions of bounded linear operators

Mohamed Boumazgour

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let T be a bounded linear operator on a Banach space X, and let M be a closed T-invariant subspace of X. In this paper, we investigate the relationships between the Drazin spectrum and the generalized Drazin spectrum of T, and those of the operators T_M and T_M, where T_M is the restriction of T to M, and T_M is the operator induced by T on the quotient space X / M.

Original language	English
Pages (from-to)	894-901
Number of pages	8
Journal	Linear and Multilinear Algebra
Volume	66
Issue number	5
DOIs	https://doi.org/10.1080/03081087.2017.1330867
State	Published - 4 May 2018
Externally published	Yes

Keywords

Drazin spectrum
generalized Drazin spectrum
Invariant subspace
operator matrices

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AB - Let T be a bounded linear operator on a Banach space X, and let M be a closed T-invariant subspace of X. In this paper, we investigate the relationships between the Drazin spectrum and the generalized Drazin spectrum of T, and those of the operators TM and TM, where TM is the restriction of T to M, and TM is the operator induced by T on the quotient space X / M.

KW - Drazin spectrum

KW - generalized Drazin spectrum

KW - Invariant subspace

KW - operator matrices

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ER -

Generalized Drazin inverse of restrictions of bounded linear operators

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Keywords

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