# Operator algebras and mathematical physics

### About this Title

**Palle E. T. Jorgensen** and **Paul S. Muhly**, Editors

Publication: Contemporary Mathematics

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

MathSciNet review: 878371

### Table of Contents

**Front/Back Matter**

- Klaus Fredenhagen – A biographical sketch of Hans-Jürgen Borchers [MR 878372]
- Marinus Winnink – A biographical sketch of N. M. Hugenholtz [MR 878373]
- Erling Størmer – A biographical sketch of Richard V. Kadison [MR 878374]
- Rudolf Haag – A biographical sketch of Daniel Kastler [MR 878375]

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

- Huzihiro Araki – Bogoliubov automorphisms and Fock representations of canonical anticommutation relations [MR 878376]
- H.-J. Borchers – On the interplay between spectrum condition and locality in quantum field theory [MR 878377]
- K. Fredenhagen – The structure of local algebras of observables [MR 878378]
- N. M. Hugenholtz – How the $C^\ast $-algebraic formulation of statistical mechanics helps understanding the approach to equilibrium [MR 878379]
- Gérard G. Emch – KMS structures in geometric quantization [MR 878380]
- Shôichirô Sakai – Perturbations and KMS states in $C^\ast $-dynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems) [MR 878381]

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

- Daniel Kastler – ${\bf Z}/2$-graded cyclic cohomology within the differential envelope [MR 878382]
- Alain Connes and Marc A. Rieffel – Yang-Mills for noncommutative two-tori [MR 878383]
- Marc A. Rieffel – Nonstable $K$-theory and noncommutative tori [MR 878384]

** IV. Positivity in Operator Algebras **

- William Arveson – Nonlinear states on $C^\ast $-algebras [MR 878385]
- Erling Størmer – Cones of positive maps [MR 878386]
- Jun Tomiyama – On the geometry of positive maps in matrix algebras [MR 878387]

** V. Dynamical Systems and Derivations **

- Derek W. Robinson – Differential operators on $C^\ast $-algebras [MR 878388]
- Ola Bratteli – Derivations and free group actions [MR 878389]
- Ola Bratteli and Akitaka Kishimoto – Automatic continuity of derivations on eigenspaces [MR 878390]
- Shôichirô Sakai – Dynamics in continuous quantum systems [MR 878391]

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

- Joachim Cuntz and Nigel Higson – Kuiper’s theorem for Hilbert modules [MR 878392]
- Gerald W. Johnson and Michel L. Lapidus – Feynman’s operational calculus, generalized Dyson series and the Feynman integral [MR 878393]
- Robert T. Powers – An index theory for continuous semigroups of $\ast $-endomorphisms of $\mathfrak {B}(\mathfrak {H})$ and ${\rm II}_1$ factors [MR 878394]
- Harald Upmeier – Multivariable Toeplitz operators, Jordan algebras and index theory [MR 878395]

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

- Edward G. Effros – On multilinear completely bounded module maps [MR 878396]
- Berndt Brenken, Joachim Cuntz, George A. Elliott and Ryszard Nest – On the classification of noncommutative tori. III [MR 878397]

- Roberto Longo – The joint modular structure of an inclusion of von Neumann algebras [MR 878398]
- Richard H. Herman and Vaughan F. R. Jones – Central sequences in crossed products [MR 878399]