scholarly journals The p-Drazin inverse for operator matrix over Banach algebras

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4597-4605
Author(s):  
Huanyin Chen ◽  
Honglin Zou ◽  
Tugce Calci ◽  
Handan Kose
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Block Operator Matrix ◽  
Block Operator

An element a in a Banach algebra A has p-Drazin inverse provided that there exists b ? comm(a) such that b = b2a,ak-ak+1b?J(A) for some k ? N. In this paper, we present new conditions for a block operator matrix to have p-Drazin inverse. As applications, we prove the p-Drazin invertibility of the block operator matrix under certain spectral conditions.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

scholarly journals Existence of solutions for a system of Chandrasekhar’s equations in Banach algebras underweak topology

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5949-5957
Author(s):  
Amor Fahem ◽  
Aref Jeribi ◽  
Najib Kaddachi
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Coupled System ◽  
Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Continuous Operators ◽  
Quadratic Integral Equations

This paper is devoted to the study of a coupled system within fractional integral equations in suitable Banach algebra. In particular, we are concerned with a quadratic integral equations of Chandrasekhar type. The existence of solutions will be proved by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty, closed and convex subset of Banach algebra where the entries are weakly sequentially continuous operators.

scholarly journals Stable perturbation in Banach algebras

2007 ◽  
Vol 83 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Yifeng Xue
Keyword(s):  
Banach Algebra ◽  
Error Estimates ◽  
Generalized Inverse ◽  
Invertible Element ◽  
Banach Algebras ◽  
Gap Function ◽  
Drazin Inverse ◽  
C Algebras ◽  
Stable Perturbation ◽  
Unital Banach Algebra

AbstractLet be a unital Banach algebra. Assume that a has a generalized inverse a+. Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.

scholarly journals ON INTEGRAL REPRESENTATIONS OF THE DRAZIN INVERSE IN BANACH ALGEBRAS

2002 ◽  
Vol 45 (2) ◽  
pp. 327-331 ◽  
Author(s):  
N. Castro González ◽  
J. J. Koliha ◽  
Yimin Wei
Keyword(s):  
Integral Representation ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Integral Representations ◽  
Subject Classification ◽  
Drazin Inverse ◽  
General Situation ◽  
Primary 46H05 ◽  
C Algebra

AbstractThe purpose of this paper is to derive an integral representation of the Drazin inverse of an element of a Banach algebra in a more general situation than previously obtained by the second author, and to give an application to the Moore–Penrose inverse in a $C^*$-algebra.AMS 2000 Mathematics subject classification:Primary 46H05; 46L05

Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg’s model type

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Afif Amar ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Operator Matrix ◽  
Model Type ◽  
Block Operator Matrix ◽  
Growing Cell ◽  
Block Operator ◽  
Abstract Boundary

AbstractIn this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberg’s model type, this last arises in growing cell populations. The entries of block operator matrix associated to this system are nonlinear and act on the Banach space X p:= L p([0, 1] × [a, b]; dµ dv), where 0 ≤ a < b < ∞; 1 < p < ∞.

scholarly journals ps-drazin inverses in banach algebras

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2125-2133
Author(s):  
Huanyin Chen ◽  
Tugce Calci
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Drazin Inverse

An element a in a Banach algebra A has ps-Drazin inverse if there exists p2 = p ? comm2(a) such that (a - p)k ? J(A) for some k ? N. Let A be a Banach algebra, and let a,b ? A have ps-Drazin inverses. If a2b = aba and b2a = bab, we prove that 1. ab ? A has ps-Drazin inverse. 2. a + b ? A has ps-Drazin inverse if and only if 1 + adb ? A has ps-Drazin inverse. As applications, we present various conditions under which a 2 x 2 matrix over a Banach algebra has ps-Drazin inverse.

scholarly journals On the pseudo drazin inverse of the sum of two elements in a Banach algebra

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2011-2022 ◽  
Author(s):  
Honglin Zou ◽  
Jianlong Chen
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Drazin Inverse ◽  
Necessary And Sufficient ◽  
Associative Rings

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

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