Results 121 to 130 of about 340 (155)
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Pseudo-Generalized Inverse and Drazin Invertibility
Results in Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lahmar, Asma, Skhiri, Haïkel
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Block representations of the generalized Drazin inverse
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dijana Mosić, Dragan S Djordjevic
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Some Results on the Symmetric Representation of the Generalized Drazin Inverse in a Banach Algebra [PDF]
Symmetry, 2019 [EN] Based on the conditions ab(2) = 0 and b pi(ab) is an element of A(d), we derive that (ab)(n), (ba)(n), and ab + ba are all generalized Drazin invertible in a Banach algebra A, where n is an element of N and a and b are elements of A.
Yonghui Qin +2 more
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Jacobson’s Lemma for Generalized Drazin–Riesz Inverses
Acta Mathematica Sinica, English Series, 2023Let \(R\) be a ring with unity and \(R^{inv}\) denote the set of all invertible elements in \(R\). A very well known result, referred to as Jacobson's lemma, states that, if \(a,b \in R\) are such that \(1-ab \in R^{inv},\) then \(1-ba \in R^{inv}\), in which case one has \((1-ba)^{-1}=1+b(a-b)^{-1}a.\) Recall that a bounded linear operator \(A\) on a ...
Hadji, Soufiane, Zguitti, Hassane
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On deriving the generalized Drazin inverse of block matrices in a Banach algebra
Quaestiones Mathematicae, 2016 This paper is devoted to the generalized Drazin inverse of a block matrix x = [a b c d] in a Banach algebra A, under specic conditions. We focus on deriving formulae for the generalized Drazin inverse of x in terms of the generalized Drazin inverses of ...
Dijana Mosić
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On the Generalized Drazin inverse of the Sum in a Banach Algebra
Quaestiones Mathematicae, 2019 The objective of this paper is to study the existence of the generalized Drazin inverse of the sum a + b of two generalized Drazin invertible elements in a Banach algebra and present explicit expressions for the generalized Drazin inverse of this sum ...
Dijana Mosić, Daochang Zhang
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Some Additive Properties of the Drazin Inverse and Generalized Drazin Inverse
Bulletin of the Iranian Mathematical SocietyThis paper investigates additive properties of the Drazin inverse and generalized Drazin inverse in a complex Banach algebras \(\mathcal{A}\). The set \(\mathcal{A}^{\text{qnil}}\) consists of all \(a \in \mathcal{A}\) such that \(a\) is quasi-nilpotent, namely, \(\sigma(a) = \{0\}\). Recall that the generalized Drazin inverse of \(a \in \mathcal{A}\),
Fei Peng +2 more
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On the Drazin inverse of block matrices and generalized Schur complement
Applied Mathematics and Computation, 2009Different expressions are well-known for the Banaksiewicz-Schur form of a matrix involving the Moore-Penrose inverse, the group inverse or the Drazin inverse. In all of these cases, the generalized Schur complement (considering the corresponding Moore-Penrose, group or Drazin block) plays an important role.
N Castro-González
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On the Generalized Drazin–Riesz Inverse for Closed Linear Operators
Mediterranean Journal of Mathematics, 2022Let \(X\) be a complex Banach space, \(B(X)\) stand for the space of bounded linear operators, and \(C(X)\) denote the space of closed linear operators, on \(X\), respectively. Let \(R(.)\) and \(D(.)\) denote the range space and the domain space, respectively. \(A \in C(X)\) is said to be generalized Drazin-Riesz invertible if there exists \(B\in B(X)\
Othman Abad, Hassane Zguitti
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Weighted generalized Drazin inverse in rings
Georgian Mathematical Journal, 2016Abstract In this paper, we introduce and investigate the weighted generalized Drazin inverse in rings.
Dijana Mosić, Dragan S Djordjevic
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