EXPLICIT SOLUTION TO THE OPERATOR EQUATION AXD + F X∗B = C OVER HILBERT C ∗ -MODULES
DOI:
https://doi.org/10.5281/gwzbbs03Abstract
In this paper, by using operator matrices, we investigate the explicit solution of the operator equation
AXD + F X∗B = C
in the general setting of the adjointable operators between Hilbert C∗-modules.
This solution is expressed in terms of the Moore-Penrose inverses of the operators A, B, D and F. The obtained results extend and generalize some known
operator equations studied previously by a number of mathematicians.
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