POSITIVE AND RE-POSITIVE SOLUTIONS TO SOME SYSTEMS OF ADJOINTABLE OPERATOR EQUATIONS OVER HILBERT C − MODULES
POSITIVE AND RE-POSITIVE SOLUTIONS TO SOME SYSTEMS OF ADJOINTABLE OPERATOR EQUATIONS OVER HILBERT C − MODULES
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DOI：
10.13001/1081-3810.1492
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发表时间：
2011
影响因子：
0.7
通讯作者：
Guang-Jing Song;Qingwen Wang
中科院分区：
文献类型：
--
作者：
Guang-Jing Song;Qingwen Wang
A necessary and sufficient condition for the existence of the general common positive solution to equations A1X = C1, XB2 = C2, A3XA � = C3, A4XA � = C4 for operators between Hilbert C � -modules is established, and an expression for the common positive solution to the equations is derived when the solvability conditions are satisfied. As an application, a new necessary and sufficient condition for the system of adjointable operator equations over Hilbert C � -modules to have a common Re-positive solution is proved. Moreover, an expression of the general Re-positive solution is derived when the consistent conditions are met. The results of this paper extend some known results in the literature.
