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Book Information:

Authors: Erik M. Alfsen and Frederic W. Shultz
Title: State spaces of operator algebras: Basic theory, orientations, and C*-products
Additional book information: Birkhäuser Boston, Boston, MA, 2001, xii + 350 pp., ISBN 0-8176-3890-3, $69.95

Authors: Erik M. Alfsen and Frederic W. Shultz
Title: Geometry of state spaces of operator algebras
Additional book information: Birkhäuser Boston, Boston, MA, 2003, xiv + 467 pp., ISBN 0-8176-4319-2, $74.95

References [Enhancements On Off] (What's this?)

  • 1. E. M. Alfsen and F. W. Shultz, State spaces of Jordan algebras, Acta Math. 140 (1978), 155-190. MR 57:12630
  • 2. E. M. Alfsen, H. Hanche-Olsen, and F. W. Shultz, State spaces of C*-algebras, Acta Math. 144 (1980), 267-305. MR 81g:46074
  • 3. J. Baez, The octonions, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, 145-205. MR 2003f:17003
  • 4. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States, Models in Quantum Statistical Mechanics (Second edition), Texts and Monographs in Physics, Springer-Verlag, Berlin, 1997. MR 98e:82004
  • 5. A. Connes, A survey of foliations and operator algebras, Operator Algebras and Applications, Part I (Kingston, Ont., 1980), pp. 521-628, Proc. Sympos. Pure Math. 38, Amer. Math. Soc., Providence, RI, 1982. MR 84m:58140
  • 6. J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), no. 3, 251-268. MR 82f:46073a
  • 7. J. Dixmier, Anneaux d'opérateurs et représentations des groupes, Séminaire Bourbaki, Vol. 1, Exp. No. 40, pp. 331-336, Soc. Math. France, Paris, 1995.
  • 8. G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Monographs and Texts in Physics and Astronomy, Wiley-Interscience, New York, 1972.
  • 9. B. Iochum and F. W. Shultz, Normal state spaces of Jordan and von Neumann algebras, J. Funct. Analysis 50 (1983), 317-328. MR 84i:46064
  • 10. V. F. R. Jones, Subfactors and Knots, CBMS Regional Conference Series in Mathematics, 80, Amer. Math. Soc., Providence, RI, 1991. MR 93b:57008
  • 11. R. V. Kadison, A representation theory for commutative topological algebra, Mem. Amer. Math. Soc. 1951, (1951), no. 7. MR 13:360b
  • 12. G. G. Kasparov, Equivariant $KK$-theory and the Novikov conjecture, Invent. Math. 91 (1988), no. 1, 147-201. MR 88j:58123
  • 13. G. G. Kasparov and G. Skandalis, Groups acting on buildings, operator $K$-theory, and Novikov's conjecture,$K$-Theory 4 (1991), no. 4, 303-337. MR 92h:19009
  • 14. W. Kaup, Jordan algebras and holomorphy, Functional Analysis, Holomorphy, and Approximation Theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978), pp. 341-365, Lecture Notes in Math., 843, Springer, Berlin, 1981. MR 82i:17026
  • 15. N. P. Landsman, Quantization as a functor, Quantization, Poisson Brackets and Beyond (Manchester, 2001), pp. 9-24, Contemp. Math. 315, Amer. Math. Soc., Providence, RI, 2002. MR 2004c:53154
  • 16. N. C. Phillips, Continuous-trace C*-algebras not isomorphic to their opposite algebras, Internat. J. Math. 12 (2001), no. 3, 263-275. MR 2002f:46110
  • 17. A. Rodríguez-Palacios, Jordan structures in analysis, Jordan Algebras (Oberwolfach, 1992), pp. 97-186, de Gruyter, Berlin, 1994. MR 95g:46095
  • 18. R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics, University of Chicago Press, Chicago, IL, 1994. MR 95i:81176

Review Information:

Reviewer: Nik Weaver
Affiliation: Washington University
Journal: Bull. Amer. Math. Soc. 41 (2004), 535-539
MSC (2000): Primary 46L30; Secondary 46L05, 46L10, 46L70
Published electronically: April 28, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society