The Drazin inverse of the sum of two bounded linear operators and it’s applications
Keyword(s):
Let P and Q be bounded linear operators on a Banach space. The existence of the Drazin inverse of P+Q is proved under some assumptions, and the representations of (P+Q)D are also given. The results recover the cases P2Q = 0,QPQ = 0 studied by Yang and Liu in [19] for matrices, Q2P = 0; PQP = 0 studied by Cvetkovic and Milovanovic in [7] for operators and P2Q + QPQ = 0, P3Q = 0 studied by Shakoor, Yang and Ali in [16] for matrices. As an application, we give representations for the Drazin inverse of the operator matrix A = (ACBD).
2019 ◽
Vol 12
(05)
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pp. 1950084
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2013 ◽
Vol 846-847
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pp. 1286-1290
2001 ◽
Vol 70
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pp. 189-198
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1996 ◽
Vol 38
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pp. 367-381
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2019 ◽
Vol 35
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pp. 171-184
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2007 ◽
Vol 82
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pp. 163-181
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2006 ◽
Vol 81
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pp. 405-423
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