2016
DOI: 10.1016/j.laa.2015.10.009
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The Bott–Duffin (e,f)-inverses and their applications

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Cited by 11 publications
(5 citation statements)
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“…After their introduction, an impressive number of papers dealt with (b, c)-inverses and inverses along an element. They have been most studied in the contexts of rings [4,5,16,36,[38][39][40]53,67,68,75,[80][81][82][83][84] and semigroups [2,14,16,[24][25][26][27][44][45][46]49], and they have been also studied in the context of Banach algebras [8,9,45], residuated semigroups and quantales [33], matrices over a field [6,15,61,70], matrices over a ring [37], tensors [59], and fuzzy matrices with entries in a complete residuated lattice [18]. Core and dual core inverses were studied in [1,43,57,69,76], in the contexts of matrices and rings, and inner and outer inverses with prescribed idempotents and ideals have been considered in [13,22,…”
Section: Introductionmentioning
confidence: 99%
“…After their introduction, an impressive number of papers dealt with (b, c)-inverses and inverses along an element. They have been most studied in the contexts of rings [4,5,16,36,[38][39][40]53,67,68,75,[80][81][82][83][84] and semigroups [2,14,16,[24][25][26][27][44][45][46]49], and they have been also studied in the context of Banach algebras [8,9,45], residuated semigroups and quantales [33], matrices over a field [6,15,61,70], matrices over a ring [37], tensors [59], and fuzzy matrices with entries in a complete residuated lattice [18]. Core and dual core inverses were studied in [1,43,57,69,76], in the contexts of matrices and rings, and inner and outer inverses with prescribed idempotents and ideals have been considered in [13,22,…”
Section: Introductionmentioning
confidence: 99%
“…It is worth noticing one of the main properties of these inverses, namely, they encompass several well known outer inverses such as the Drazin inverse, the group inverse and the Moore-Penrose inverse. Furthermore, several authors have studied these notions, see for the (b, c)-inverse [4,6,8,9,14,15,25,30] and for the invese along an element [1, 2, 19-22, 32, 33]. In particular, in [4] and [2] several properties of the (b, c)-inverse and the inverse along an element were studied in the Banach context, respectively.…”
Section: Introductionmentioning
confidence: 99%
“…According to what has been said, if a ∈ A is Bott-Duffin (p, q)-invertible, then the element y in Definition 2.2 will be denoted by a −(p, q) . To learn more on the outer inverses recalled in Definition 2.1 and Definition 2.2, see [4,6,8,9,14,15,25,30].…”
Section: Introductionmentioning
confidence: 99%
“…As it was pointed out in [9], this inverse generalizes among others the standard inverse, the Drazin inverse, and the Moore-Penrose inverse. To learn more on this inverse, see [5,6,9,10,12].…”
Section: Introduction and Notationmentioning
confidence: 99%