Noncommutative Probability and Applications
Stanley Gudder · Birkhäuser Boston eBooks · 2004
Various versions of noncommutative probability theory are surveyed. It is stressed that the main motivation and applications of these noncommutative theories is quantum mechanics. A review of traditional probability theory and its unsharp version are presented. Sharp and unsharp Hilbert space probability theories are considered next. We then present a general discussion of observables and statistical maps. Finally, we consider sequential effect algebras and show that they unify and generalize all of these types of probability theories.