Solutions to the System of Operator Equations A1X = C1, XB2 = C2, and A3XB3 = C3 on Hilbert C*‐Modules

Xiaochun Fang, Enran Hou and Ge Dong

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We study the solvability of the system of the adjointable operator equations A1X = C1, XB2 = C2, and A3XB3 = C3 over Hilbert C*‐modules. We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system. We also derive representations for a general solution and a positive solution to this system. The above results generalize some recent results concerning the equations for operators with closed ranges.

Date: 2013
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https://doi.org/10.1155/2013/826564

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:826564

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