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Book Review
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Book Information
Author(s):
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,
$69.95,
0-8176-3890-3
Author(s):
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,
$74.95,
0-8176-4319-2
References:
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- 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
 -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
 -theory, and Novikov's conjecture, -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
Additional Information:
Reviewer(s):
Nik
Weaver
Affiliation:
Washington University
Email:
nweaver@math.wustl.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
41
(2004),
535-539.
MSC
(2000):
Primary 46L30;
Secondary 46L05, 46L10, 46L70
DOI:
10.1090/S0273-0979-04-01019-5
PII:
S 0273-0979(04)01019-5
Posted:
April 28, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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