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 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

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.

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.

scholarly journals Additive property of pseudo Drazin inverse of elements in Banach algebras

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1773-1781
Author(s):  
Huihui Zhu ◽  
Jianlong Chen
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Drazin Inverse ◽  
Additive Property ◽  
Equivalent Conditions

This article concerns the pseudo Drazin inverse of the sums (resp. differences) and the products of elements in a Banach algebra A. Some equivalent conditions for the existence of the pseudo Drazin inverse of a + b (resp. a - b) are characterized. Moreover, the representations for the pseudo Drazin inverse are given. Some related known results are generalized.

scholarly journals Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xiaoji Liu ◽  
Xiaolan Qin
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Block Matrix ◽  
Drazin Inverse ◽  
The Subject ◽  
Generalized Drazin Inverse

We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject.

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

2021 ◽  
pp. 1-12
Author(s):  
PRAKASH A. DABHI ◽  
DARSHANA B. LIKHADA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Discrete Groups ◽  
Discrete Semigroups ◽  
Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

scholarly journals Compact linear operators from an algebraic standpoint

1967 ◽  
Vol 8 (1) ◽  
pp. 41-49 ◽  
Author(s):  
F. F. Bonsall
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Linear Operators ◽  
Identity Operator ◽  
Algebra Structure ◽  
Natural Setting ◽  
Norm Topology ◽  
Bounded Linear ◽  
Underlying Space ◽  
Closed Subalgebra

Let B(X) denote the Banach algebra of all bounded linear operators on a Banach space X. Let t be an element of B(X), and let edenote the identity operator on X. Since the earliest days of the theory of Banach algebras, ithas been understood that the natural setting within which to study spectral properties of t is the Banach algebra B(X), or perhaps a closed subalgebra of B(X) containing t and e. The effective application of this method to a given class of operators depends upon first translating the data into terms involving only the Banach algebra structure of B(X) without reference to the underlying space X. In particular, the appropriate topology is the norm topology in B(X) given by the usual operator norm. Theorem 1 carries out this translation for the class of compact operators t. It is proved that if t is compact, then multiplication by t is a compact linear operator on the closed subalgebra of B(X) consisting of operators that commute with t.

scholarly journals Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra

2010 ◽  
Vol 432 (8) ◽  
pp. 1885-1895 ◽  
Author(s):  
N. Castro-González ◽  
M.F. Martínez-Serrano
Keyword(s):  
Banach Algebra ◽  
Drazin Inverse
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