Additive Results for the Generalized Drazin Inverse in a Banach Algebra

Mosić, Dijana

doi:10.1007/s40840-015-0143-z

Cited by 11 publications

(6 citation statements)

References 12 publications

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“…In Section 2, we prove that a + b has generalized Drazin inverse and the explicit formula for (a + b) d is obtained. This extend the result of [11,Theorem 2.2].…”

Section: Introductionsupporting

confidence: 89%

“…In Section 3, we characterize the generalized Drazin inverse of an element based on its pierce decomposition. These extend the result of [11,Theorem 3.1] to more general setting. If a ∈ A has g-Drazin inverse a d .…”

Section: Introductionsupporting

confidence: 79%

“…The g-Drazin invertiblity of the sum of two elements has a rich history. It was extensively studied in matrix and operator theory by many authors, e.g., [1,2,5,7,8,10,11,12] and [13]. In this paper we study this topic under the weaker conditions and extend the main results of [11].…”

mentioning

confidence: 79%

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The g-Drazin inverse of the sum in Banach algebras

Chen

Sheibani

2020

Linear and Multilinear Algebra

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We explore the generalized Drazin inverse in a Banach algebra. Let A be a Banach algebra, and let a, b ∈ A d . If ab = λa π bab π then a + b ∈ A d . The explicit representation of (a + b) d is also presented. As applications of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. The main results of Liu and Qin [Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices, Sci. World J., 2015, 156934.8] are extended.2010 Mathematics Subject Classification. 15A09, 47L10, 32A65.

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“…In Section 2, we prove that a + b has generalized Drazin inverse and the explicit formula for (a + b) d is obtained. This extend the result of [11,Theorem 2.2].…”

Section: Introductionsupporting

confidence: 89%

Section: Introductionsupporting

confidence: 79%

See 1 more Smart Citation

The g-Drazin inverse of the sum in Banach algebras

Chen

Sheibani

2020

Linear and Multilinear Algebra

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“…It follows from [7,Theorem 4.2] that 0 / ∈ σ d (a) if and only if 0 / ∈ acc σ(a). More interesting properties of the g-Drazin inverse can be found in a recent papers [4,8,9].…”

Section: Introductionmentioning

confidence: 86%

A new extension of generalized Drazin inverse in Banach algebras

Ren¹,

Jiang²

2022

Preprint

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In this paper, we introduce and study a new generalized inverse, called ag-Drazin inverses in a Banach algebra A with unit 1. An element a ∈ A is ag-Drazin invertible if there exists x ∈ A such that ax = xa, xax = x and a − axa ∈ A acc , where A acc {a ∈ A : a − λ1 is generalized Drazin invertible for all λ ∈ C\{0}}. Using idempotent elements, we characterize this inverse and give some its representations. Also, we prove that a ∈ A is ag-Drazin invertible if and only if 0 is not an accumulation point of σd(a), where σd(a) is the generalized Drazin spectrum of a.

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“…The g-Drazin invertibility of the sum of two elements in a Banach algebra is attractive. Many authors have studied such problems from many different views, e.g., [3,4,6,7,11,13,15,17]. In Section 2, we investigate when the sum of two g-Drazin invertible elements in a Banach algebra has g-Drazin inverse.…”

Section: Introductionmentioning

confidence: 99%

Expressions for the g-Drazin inverse in a Banach algebra

Chen

Sheibani

2020

Filomat

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We explore the generalized Drazin inverse in a Banach algebra. Let A be a Banach algebra, and let a,b ? Ad. If ab = ?a?bab? for a nonzero complex number ?, then a + b ? Ad. The explicit representation of (a + b)d is presented. As applications of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. The main results of Liu and Qin [Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices, Sci. World J., 2015, 156934.8] are extended.

show abstract

Additive Results for the Generalized Drazin Inverse in a Banach Algebra

Cited by 11 publications

References 12 publications

The g-Drazin inverse of the sum in Banach algebras

The g-Drazin inverse of the sum in Banach algebras

A new extension of generalized Drazin inverse in Banach algebras

Expressions for the g-Drazin inverse in a Banach algebra

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