On the Equivalence of the Operator Equations XA + BX = C and X - p(-B)Xp(A)(-1) = W in a Hilbert-Space, p A Polynomial
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چکیده
We consider the solution of (∗) XA + BX = C for bounded operators A, B, C and X on a Hilbert space, A normal. We establish the existence of a polynomial p and a bounded operator W with the property that the unique solution X of (∗) also solves X − p(−B)Xp(A)−1 = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (∗).
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تاریخ انتشار 2015