The generalized Drazin inverse of the sum in a Banach algebra
نویسندگان
چکیده
منابع مشابه
Generalized Drazin inverse of certain block matrices in Banach algebras
Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.
متن کاملRepresentations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices
We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.
متن کاملExpressions for the generalized Drazin inverse of a block matrix in a Banach algebra
We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.
متن کاملGroup Inverse and Generalized Drazin Inverse of Block Matrices in a Banach Algebra
Let A be a complex unital Banach algebra with unit 1. The sets of all invertible and quasinilpotent elements (σ(a) = {0}) of A will be denoted by A and A, respectively. The group inverse of a ∈ A is the unique element a ∈ A which satisfies aaa = a, aaa = a, aa = aa. If the group inverse of a exists, a is group invertible. Denote by A the set of all group invertible elements of A. The generalize...
متن کاملThe generalized Drazin inverse with commutativity up to a factor in a Banach algebra
In this paper, we investigate an explicit representation of the generalized Drazin inverse (a ± b) d in terms of a, a d , b and b d under the condition ab = λba or ab = aba and extend to Banach algebras recent results of C.Y. Deng.
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ژورنال
عنوان ژورنال: Annals of Functional Analysis
سال: 2017
ISSN: 2008-8752
DOI: 10.1215/20088752-3764461