The pseudo core inverses of differences and products of projections in rings with involution

Chen, Xiaofeng; Chen, Jianlong; Zhou, Yukun

doi:10.2298/fil2101181c

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2023

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Cited by 3 publications

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“…The core-EP invertibility in a Banach *-algebra is attractive. We refer to reader for the various properties of core-EP inverse in [12,14,15,16,26].…”

Section: Introductionmentioning

confidence: 99%

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

Chen,

Abdolyousefi

2023

Preprint

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In this paper, we introduce the notion of the generalized weighted core inverse in a Banach *-algebra. We characterize this new generalized inverse by using the generalized weighted core decomposition and present the representations by the generalized Drazin inverse. These extend the core-EP inverse and weighted (pseudo) core inverse for complex matrices and linear bounded operators to more general setting. 2020 Mathematics Subject Classification. 15A09, 16U90, 46H05.

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“…The core-EP invertibility in a Banach *-algebra is attractive. We refer to reader for the various properties of core-EP inverse in [12,14,15,16,26].…”

Section: Introductionmentioning

confidence: 99%

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

Chen,

Abdolyousefi

2023

Preprint

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

Chen,

Abdolyousefi

2023

Preprint

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Jacobson’s lemma and Cline’s formula for weighted generalized inverses in a ring with involution

Zhou,

Chen

2023

Filomat

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Let R be a ring with involution and e, f ? R be Hermitian and invertible. We first present some equivalent conditions for paq to be {1, 3 f }-invertible, assuming that p, a, q ? R with p?pa = a = aqq? for some p?, q? ? R and a is {1, 3e}-invertible. Then, these results are applied to give the sufficient and necessary conditions under which Jacobson?s lemma and Cline?s formula for weighted pseudo core inverses hold. Also, Jacobson?s lemma for weighted Moore-Penrose inverses is investigated.

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The pseudo core inverses of differences and products of projections in rings with involution

Cited by 3 publications

References 9 publications

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

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

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

Jacobson’s lemma and Cline’s formula for weighted generalized inverses in a ring with involution

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