On Jacobson’s lemma and Drazin invertibility
نویسندگان
چکیده
منابع مشابه
Drazin Invertibility of Products
If a and b are elements of an algebra, then we show that ab is Drazin invertible if and only if ba is Drazin invertible. With this result we investigate products of bounded linear operators on Banach spaces. 1. Drazin inverses Throughout this section A is a real or complex algebra with identity e 6= 0. We denote the group of invertible elements of A by A. We call an element a ∈ A relatively reg...
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The paper deals with the generalized Drazin invertibility of combinations of idempotents p, q in a Banach algebra. It proves the equivalence of the generalized Drazin invertibility of p−q and p+q, as well as the equivalence of the generalized Drazin invertibility of the commutator pq − qp and anticommutator pq + qp of p, q. It extends several results of J. Math. Anal. Appl. 359 (2009) 731–738, ...
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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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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2010
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.11.009