Probability operator and convolution semigroups of instruments in quantum probability (Q1116563)

In quantum measurement theory a central notion is that of instrument, which is a certain kind of operator-valued measure. In this paper instruments on locally compact groups are studied; as in classical probability theory, probability operators associated with instruments are introduced and characterized. The notion of probability operator is formulated in such a way that probability operators turn out to be transition maps on certain \(W^*\)-algebras. Then, the generator of a norm continuous semigroup of probability operators is characterized.