  In this paper, we solve a spectral problem about positive semi-definite
trace-class pseudodifferential operators on modulation spaces which was posed
by H. Feichtinger. Later, C. Heil and D. Larson rephrased the problem in the
broader setting of positive semi-definite trace-class operators on a separable
Hilbert space. Our solution consists in constructing a counterexample that
solves Hans Feichtinger's problem by first solving this second problem.
