Common hermitian and positive solutions to the adjointable operator equations , |
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Authors: | Qingxiang Xu |
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Institution: | aDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, PR China |
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Abstract: | Let be a C*-algebra. For any Hilbert -modules H and K, let be the set of adjointable operators from H to K. Let H,K,L be Hilbert -modules, and . In this paper, we propose necessary and sufficient conditions for the existence of common hermitian and positive solutions to the equations , and obtain the formulae for the general forms of these solutions. Some results, known for finite matrices and Hilbert space operators, are extended to the adjointable operators acting on Hilbert C*-modules. |
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Keywords: | Hilbert C*-module Moore–Penrose inverse Inner inverse Equations AX = C and XB = D Hermitian solution Positive solution |
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