scholarly journals On the weighted pseudo Drazin invertible elements in associative rings and Banach algebras

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6359-6367
Author(s):  
Jianlong Chen ◽  
Xiaofeng Chen ◽  
Hassane Zguitti
Keyword(s):  
Banach Algebras ◽  
Drazin Inverse ◽  
Invertible Elements ◽  
Associative Rings ◽  
Equivalent Conditions

In this paper, we introduce and investigate the weighted pseudo Drazin inverse of elements in associative rings and Banach algebras. Some equivalent conditions for the existence of the w-pseudo Drazin inverse of a + b are given. Using the Pierce decomposition, the representations for the w-pseudo Drazin inverse are given in Banach algebras.

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 Rank and the Drazin inverse in Banach algebras

2006 ◽  
Vol 177 (3) ◽  
pp. 211-224 ◽  
Author(s):  
R. M. Brits ◽  
L. Lindeboom ◽  
H. Raubenheimer
Keyword(s):  
Banach Algebras ◽  
Drazin Inverse

Properties of generalized strongly Drazin invertible elements in general rings

2017 ◽  
Vol 16 (11) ◽  
pp. 1750207 ◽  
Author(s):  
Orhan Gürgün
Keyword(s):  
General Setting ◽  
Drazin Inverse ◽  
Invertible Elements ◽  
General Ring

In this paper, we define the generalized strong Drazin inverse in a general ring and investigate this class of inverses. Thus, recent results on the strong Drazin invertible and generalized strong Drazin invertible elements are extended to a more general setting. In particular, we show that [Formula: see text] is generalized strong Drazin invertible in a general ring [Formula: see text] if and only if there exists an idempotent [Formula: see text] such that [Formula: see text] and [Formula: see text] is quasinilpotent in [Formula: see text]. We also prove that if [Formula: see text] is generalized Drazin invertible in [Formula: see text] for some [Formula: see text], so are [Formula: see text], [Formula: see text], [Formula: see text]. This partially answer to a question posed by Mosić.

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

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