Continuous versions of an inequality due to Hoffman and Wielandt (Q1086803)

The author proves the following theorem: Let A and B be completely continuous operators on a Hilbert space H belonging to the Schmidt class with eigenvalues \(\{\alpha_ i\}\) and \(\{\beta_ i\}\) respectively, taking account of their multiplicities. If \(A\geq 0\), and B is normal with Re\((B)\geq 0\), then there exists a suitable numbering of the eigenvalues such that \[ \sum^{\infty}_{i=1}| \alpha_ i-\beta_ i|^ 2\leq \| A-B\|^ 2. \]