Chapter 46: von Neumann Algebras

The following sections are included:

• Basics of von Neumann Algebras

  • Locally Convex Topologies on ℒ(ℋ)

  • Definition and Some Elementary Properties of General von Neumann Algebras

  • Predual and Normal States

• Spectral and Classificatory Notions

  • Arveson Spectrum and Borchers–Arveson Theorem

  • Quasiequivalence, Disjointness, and Folia

  • Faces, Projections, Supports, and Equivalence

• Modular Theory and Thermal Fields

  • Standard von Neumann Algebras

  • Standard Implementation of Automorphisms