Assuming only that the spectra of A and B are disjoint as opposed to the more restrictive assumption previously used, we obtain a bound in all unitarily invariant norms on the solution to the structured Sylvester equation AX − XB = A1/2EB1/2. This bound is the first of its kind in all unitarily invariant norms under only the disjointedness assumption. An application of the bound to the relative...