  Given two trace class operators A and B on a separable Hilbert space we
provide an upper bound for the Hausdorff distance of their spectra involving
only the distance of A and B in operator norm and the singular values of A and
B. By specifying particular asymptotics of the singular values our bound
reproduces or improves existing bounds for the spectral distance. The proof is
based on lower and upper bounds for determinants of trace class operators of
independent interest.
