We present necessary and sufficient conditions for the existence of a positive solution to the system of adjointable operator equations We also derive a representation for a general positive solution to this system when the solvability conditions are satisfied. The results of this paper extend some
โฆ LIBER โฆ
Solutions to operator equations on Hilbert -modules
โ Scribed by Xiaochun Fang; Jing Yu; Hongliang Yao
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 177 KB
- Volume
- 431
- Category
- Article
- ISSN
- 0024-3795
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In this paper, we study the solvability of the operator equation AXB \* -BX \* A \* = C in the general setting of the adjointable operators between Hilbert C \* -modules. Based on the generalized inverses of the associated operators, we propose the necessary and sufficient conditions for the existen