On metric controlled operator-valued frames and their applications

The exploration of pseudo-Hermitian quantum mechanics has led to rapid progress in the methods of constructing inner products and determining the observables of the theory in quantum sciences. In this paper, we introduce metric controlled operator-valued frames and our motivation is to find the applications in the generalized setting of quantum mechanics. We give various characterizations of metric controlled operator-valued frames. We also explore various spectral properties of pseudo-Hermitian and pseudo-unitary operators. Finally, we give the method of representing infinte quantum channels in pseudo-Hermitian quantum mechanics using metric controlled operator-valued frames.