Transition Probabilities of Positive Linear Functionals on $\ast$-Algebras

Abstract

Using unbounded Hilbert space representations basic results on the transition probability of positive linear functionals $f$ and $g$ on a unital *-algebra are obtained. The main assumption is the essential self-adjointness of GNS representations ${\pi }_f$ and ${\pi }_g$. Applications to functionals given by density matrices and by integrals and to vector functionals on the Weyl algebra are given.

References in corpus (1)

• Geometric Mean of States and Transition Amplitudes