The g-Hirano inverse in Banach algebras

Chen, Huanyin; Sheibani, Marjan

doi:10.1080/03081087.2019.1627278

Cited by 7 publications

(23 citation statements)

References 13 publications

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“…In [3,4], the authors introduced and studied generalized core-EP inverse and generalized group inverse for an element in a Banach *-algebra. An element a ∈ A has generalized core-EP inverse if there exists a x ∈ A such that…”

Section: Huanyin Chen and Marjan Sheibani *mentioning

confidence: 99%

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On generalized core invertibility in Banach algebras

Chen,

Sheibani

2023

Preprint

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We introduce a new generalized inverse, called generalized core inverse in a Banach *-algebra. This new inverse is an extension of weak core inverse defined for complex square matrix and bounded linear operators over Hilbert spaces. We present various characterizations of this new inverse. The relationship between the generalized core inverse and other generalized inverses is investigated. Finally, we consider the necessary and sufficient conditions under which generalized core inverse and generalized core-EP inverse coincide with each other in a Banach *-algebra.

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Section: Huanyin Chen and Marjan Sheibani *mentioning

confidence: 99%

“…Such x is unique if it exists, and denote it by a d ❖ (see [3]). An element a ∈ A has generalized group inverse if there exists a x ∈ A such that…”

Section: Huanyin Chen and Marjan Sheibani *mentioning

confidence: 99%

On generalized core invertibility in Banach algebras

Chen,

Sheibani

2023

Preprint

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“…We call a has generalized core-EP inverse if it has generalized 1-core-EP inverse and denote a d ❖,1 by a d ❖ . Many properties of generalized core-EP inverse are presented in [1].…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.2. (see [1,Theorem 1.2]) Let A be a Banach *-algebra, and let a ∈ A. Then the following are equivalent:…”

Section: Introductionmentioning

confidence: 99%

Weighted generalized core-EP inverse in a Banach algebra with involution

Chen,

Sheibani

2023

Preprint

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In this paper, we introduce the notion of weighted generalized core-EP inverse in a Banach *-algebra. Some properties of weighted core-EP inverse for rectangular complex matrices and bounded linear Hilbert space operators are generalized and some new ones are established. Properties of weighted generalized core-EP orders are presented for all weighted g-Drazin invertible elements in a Banach *-algebra. 2020 Mathematics Subject Classification. 46H05, 15A09, 16U99

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“…In [2,6,11] and [14], Chen et al studied such generalized inverse for n = 1. In [3,4] and [5], the authors investigated this generalized inverse for n = 2. For a Banach algebra A, we proved that a ∈ A has generalized 2-strongly Drazin inverse if and only if a − a 3 ∈ A qnil if and only if a is the sum of a tripotent and a quasinilpotent that commute (see [5,Theorem 2.4 and Theorem 2.7]).…”

Section: Introductionmentioning

confidence: 99%