# Operator algebras and mathematical physics

### About this Volume

Edited by: Palle E. T. Jorgensen and Paul S. Muhly

Publication Year
1987: Volume: 62

ISBNs: 978-0-8218-5066-4 (print); 978-0-8218-7652-7 (online)

DOI: http://dx.doi.org/10.1090/conm/062

### Table of Contents

**Front/Back Matter**

**I. Biographical Sketches**

- Klaus Fredenhagen – A biographical sketch of Hans-Jürgen Borchers
- Marinus Winnink – A biographical sketch of N. M. Hugenholtz
- Erling Størmer – A biographical sketch of Richard V. Kadison
- Rudolf Haag – A biographical sketch of Daniel Kastler

**II. The Algebraic Approach to Quantum Theory of Fields and Statistical Mechanics**

- Huzihiro Araki – Bogoliubov automorphisms and Fock representations of canonical anticommutation relations
- H.-J. Borchers – On the interplay between spectrum condition and locality in quantum field theory
- K. Fredenhagen – The structure of local algebras of observables
- N. M. Hugenholtz – How the $C^\ast $-algebraic formulation of statistical mechanics helps understanding the approach to equilibrium
- Gérard G. Emch – KMS structures in geometric quantization
- Shôichirô Sakai – Perturbations and KMS states in $C^\ast $-dynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems)

**III. Methods from Differential Geometry and $K$-theory**

- Daniel Kastler – ${\bf Z}/2$-graded cyclic cohomology within the differential envelope
- Alain Connes and Marc A. Rieffel – Yang-Mills for noncommutative two-tori
- Marc A. Rieffel – Nonstable $K$-theory and noncommutative tori

**IV. Positivity in Operator Algebras**

- William Arveson – Nonlinear states on $C^\ast $-algebras
- Erling Størmer – Cones of positive maps
- Jun Tomiyama – On the geometry of positive maps in matrix algebras

**V. Dynamical Systems and Derivations**

- Derek W. Robinson – Differential operators on $C^\ast $-algebras
- Ola Bratteli – Derivations and free group actions
- Ola Bratteli and Akitaka Kishimoto – Automatic continuity of derivations on eigenspaces
- Shôichirô Sakai – Dynamics in continuous quantum systems

**VI. Operators in Hilbert Spaces: Some Algebraic Methods**

- Joachim Cuntz and Nigel Higson – Kuiper’s theorem for Hilbert modules
- Gerald W. Johnson and Michel L. Lapidus – Feynman’s operational calculus, generalized Dyson series and the Feynman integral
- Robert T. Powers – An index theory for continuous semigroups of $\ast $-endomorphisms of $\mathfrak {B}(\mathfrak {H})$ and ${\rm II}_1$ factors
- Harald Upmeier – Multivariable Toeplitz operators, Jordan algebras and index theory

**VII. $C^*$-Algebras: Some Recent Results**

- Edward G. Effros – On multilinear completely bounded module maps
- Berndt Brenken, Joachim Cuntz, George A. Elliott and Ryszard Nest – On the classification of noncommutative tori. III

**VIII. Von Neumann Algebras**