Further results on Left and Right Generalized Drazin Invertible Operators

So. Messirdi; Sa. Messirdi; B. Messirdi

doi:10.30970/ms.54.1.98-106

So. Messirdi Department of Mathematics and Informatics, University of Mostaganem
Sa. Messirdi High Industrial Institute for Social Promotion ISIPS-Hainaut
B. Messirdi High School of Electrical and Energetic Engineering-Oran

DOI: https://doi.org/10.30970/ms.54.1.98-106

Анотація

In this paper we present some new characteristics and expressions of left and right generalized Drazin invertible bounded operators on a Banach space $X.$ An explicit formula relating the left and the right generalized Drazin inverses to spectral idempotents is provided. In addition, we give a characterization of operators in $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) with equal spectral idempotents, where $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) denotes the set of all left (resp. right) generalized Drazin invertible bounded operators on $X.$ Next, we give some sufficient conditions which ensure that the product of elements of $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) remains in $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$). Finally, we extend Jacobson's lemma for left and right generalized Drazin invertibility. The provided results extend certain earlier works given in the literature.

Біографії авторів

So. Messirdi, Department of Mathematics and Informatics, University of Mostaganem

Department of Mathematics and Informatics, University of Mostaganem. Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO)

Sa. Messirdi, High Industrial Institute for Social Promotion ISIPS-Hainaut

High Industrial Institute for Social Promotion ISIPS-Hainaut

B. Messirdi, High School of Electrical and Energetic Engineering-Oran

High School of Electrical and Energetic Engineering-Oran
Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO)
University of Oran1, Ahmed Benbella, Algeria

Посилання

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