Conditions for the completeness of the spectral domain of a harmonizable process

We generalize a theorem of Kِthe and Toeplitz on unconditional bases in Hilbert spaces to Hilbert space-valued measures. This leads to a necessary and sufficient condition for the completeness of the spectral domain of a weakly harmonizable process whose shift operator exists and is invertible. A process in this class has a complete spectral domain if and only if it is the image of a stationary process under a topological isomorphism.