Group inverse and core inverse in Banach and <i>C</i>*-algebras

Mihajlović, Nadica

doi:10.1080/00927872.2019.1705475

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Cited by 11 publications

(9 citation statements)

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“…If such x exists, it is unique, and denote it by a # ○ . Recently, many authors have studied core and core-EP inverses from many different views, e.g., [5,7,8,14,17,24,27,28,31].…”

Section: Introductionmentioning

confidence: 99%

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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“…If such x exists, it is unique, and denote it by a # ○ . Recently, many authors have studied core and core-EP inverses from many different views, e.g., [5,7,8,14,17,24,27,28,31].…”

Section: Introductionmentioning

confidence: 99%

On generalized core invertibility in Banach algebras

Chen,

Sheibani

2023

Preprint

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“…We use A # ⃝ to denote the set of all core invertible elements in A. The core inverse has been studied by many authors from different point of views (see [1,17,18,19,22,24,25]).…”

Section: Introductionmentioning

confidence: 99%

The generalized core-EP inverses involvoing projections in Banach *- algebra

Chen,

Abdolyousefi

2023

Preprint

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“…It has interesting applications of resistance distances to the bipartiteness of graphs (see [15]). Many authors have studied group invertibility from many different views, e.g., [2,3,4,5,6,12,13,14,17,18]. It was also extensively investigated under the concept "strongly regularity" in ring theory (see [7]).…”

Section: Introductionmentioning

confidence: 99%