Solutions to some solvable modular operator equations
Abstract
We find explicit solution of the operator equation $TXT^* -SXS^*=A$ in
the general setting of the adjointable operators between Hilbert
$C^*$-modules, using some block operator matrices. Furthermore, we obtain solutions to the solvable
operator equation $TXR-SY Q = A $ over Hilbert $C^*$-modules, when both
${\rm ran}(T)+{\rm ran}(S)$ and ${\rm ran}(R^*)+{\rm ran}(Q^*)$ are
closed.
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