to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The
theory of von Neumann algebras was initiated in a series of papers by Murray and von …

This is an English edition of Dixmier's book, which is the first systematic exposition of the
algebraic approach to representations of Lie groups via representations of (or modules over) …

A systematic exposition of Baer*-Rings, with emphasis on the ring-theoretic and lattice-
theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio …

We give a classification, up to unitary equivalence, of the representations of the C*-algebra
of the Canonical Commutation Relations which generalizes the classical Stone–von …

Recall that a monotone sequentially closed C* algebra (MSC for short) is a C* algebra in
which every norm-bounded increasing sequence has a least upper bound, and that a Baire …

For each derivation δ of a C∗-algebra A with δ (x∗)=− δ (x)∗ there exists a minimal positive
element h in the enveloping von Neumann algebra A′′ such that δ (x)= hx− xh. It is shown …

We recall that a Baire* algebra is a monotone σ-closed C* algebra [5], and a Σ* algebra is a
weakly σ-closed C* algebra [2](probably the notions coincide). A functional on a Baire …

A certain generalization of the mathematical formalism of quantum mechanics beyond
operator algebras is considered. The approach is based on the concept of conditional …

Sets of simple observables in the operational approach to quantum theory Page 1 ANNALES DE
L’IHP, SECTION A CM EDWARDS Sets of simple observables in the operational approach to …

In the usual partially ordered vector space approach to the theory of statistical physical
systems the set of states of the sys-tem under consideration is represented by a norm closed …