Cline’s formula for g-Drazin inverses in a ring
نویسندگان
چکیده
منابع مشابه
Jacobson’s Lemma for Drazin Inverses
If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....
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For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...
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In this paper, some additive results on Drazin inverse of a sum of Drazin invertible elements are derived. Some converse results are also presented.
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Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a polynomial in A.
متن کاملCline’s formula for the generalized Drazin inverse
†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...
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ژورنال
عنوان ژورنال: Filomat
سال: 2019
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1908249c