Les algèbres d'opérateurs dans l'espace Hilbertien (algèbres de von Neumann)

TL;DR: In this article, the authors provide a mathematical framework for the process of making repeated measurements on continuous observables in a statistical system and make a mathematical definition of an instrument, a concept which generalises the notion of an observable and that of an operation.

TL;DR: In this paper, the formalism developed in previous papers is simplified and generalized to systems with superselection rules, which describes a rather general class of linear mappings of states (density matrices).

TL;DR: In this article, the authors studied the representation of the C*-algebra of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ and showed that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant.