Before revision: One easily checks one direction: If AX − XB = C then Roth's removal rule does not generalize to infinite-dimensional bounded operators on a Banach space.Bhatia and Rosenthal, p.3
After revision: Nevertheless, Roth's removal rule generalizes to the systems of Sylvester equations.One easily checks one direction: If AX − XB = C then Roth's removal rule does not generalize to infinite-dimensional bounded operators on a Banach space.Bhatia and Rosenthal, p.3