New additive results for the generalized Drazin inverse |
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| Authors: | Chun-yuan Deng Yi-min Wei |
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| Institution: | a College of Mathematics Science, South China Normal University, Guangzhou 510631, PR China
b School of Mathematical Sciences, Fudan University, Shanghai Key Laboratory of Contemporary Applied Mathematics, Shanghai, 200433, PR China |
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| Abstract: | In this paper, we investigate additive properties of generalized Drazin inverse of two Drazin invertible linear operators in Banach spaces. Under the commutative condition of PQ=QP, we give explicit representations of the generalized Drazin inverse d(P+Q) in term of P, Pd, Q and Qd. We consider some applications of our results to the perturbation of the Drazin inverse and analyze a number of special cases. |
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| Keywords: | Generalized Drazin inverse Additive result Banach algebra |
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