On the Drazin inverses involving power commutativity |
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Authors: | Chun Yuan Deng |
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Affiliation: | School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | We explore the Drazin inverses of bounded linear operators with power commutativity (PQ=QmP) in a Hilbert space. Conditions on Drazin invertibility are formulated and shown to depend on spectral properties of the operators involved. Moreover, we prove that P±Q is Drazin invertible if P and Q are dual power commutative (PQ=QmP and QP=PnQ) and show that the explicit representations of the Drazin inverse D(P±Q) depend on the positive integers m,n?2. |
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Keywords: | Drazin inverse Power-commutativity Dual power commutativity |
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