Book Review
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Book Information:
Author:
Kenneth R. Davidson
Title:
-algebras by example
Additional book information:
Field Institute Monographs, vol. 6,
Amer. Math. Soc., Providence, RI,
1996,
xiv+309 pp.,
ISBN 0-8218-0599-1,
$59.00$
1. Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics 2, second edition, Springer-Verlag, New York, 1996.
2. Connes, A., Noncommutative Geometry, Academic Press, San Diego, 1994.
Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
Peter A. Fillmore, A user’s guide to operator algebras, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1996. A Wiley-Interscience Publication. MR 1385461
Nigel Higson, $C^*$-algebra extension theory and duality, J. Funct. Anal. 129 (1995), no. 2, 349–363. MR 1327182, DOI 10.1006/jfan.1995.1054
Kjeld Knudsen Jensen and Klaus Thomsen, Elements of $KK$-theory, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 1991. MR 1124848, DOI 10.1007/978-1-4612-0449-7
Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. II, Pure and Applied Mathematics, vol. 100, Academic Press, Inc., Orlando, FL, 1986. Advanced theory. MR 859186, DOI 10.1016/S0079-8169(08)60611-X
Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. III, Birkhäuser Boston, Inc., Boston, MA, 1991. Special topics; Elementary theory—an exercise approach. MR 1134132, DOI 10.1007/978-1-4612-3212-4
Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. IV, Birkhäuser Boston, Inc., Boston, MA, 1992. Special topics; Advanced theory—an exercise approach. MR 1170351, DOI 10.1007/978-1-4612-2968-1_{1}
George W. Mackey, The mathematical foundations of quantum mechanics: A lecture-note volume, W. A. Benjamin, Inc., New York-Amsterdam, 1963. MR 0155567
Gerard J. Murphy, $C^*$-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990. MR 1074574
N. E. Wegge-Olsen, $K$-theory and $C^*$-algebras, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. A friendly approach. MR 1222415
- 1.
- Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics 2, second edition, Springer-Verlag, New York, 1996.
- 2.
- Connes, A., Noncommutative Geometry, Academic Press, San Diego, 1994.
- 3.
- Dixmier, J., Les Algèbres d'Opérateurs dans l'Espace Hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris, 1957. MR 0094722
- 4.
- -, Les
-algèbres et leurs Représentations, Gauthier-Villars, Paris, 1964. MR 0171173
- 5.
- Fillmore, P. A., A User's Guide to Operator Algebras, Canadian Mathematical Society series of monographs and advanced texts, Wiley-Interscience, 1996. MR 1385461
- 6.
- Higson, N.,
-algebra extension theory and duality, J. Funct. Anal. 129 (1995), 349-363. MR 1327182
- 7.
- Jensen, K. K. and Thomsen, K., Elements of
-theory, Birkhäuser, Boston, 1991. MR 1124848
- 8.
- Kadison, R. and Ringrose, J., Fundamentals of the Theory of Operator Algebras, vol. I, Academic Press, New York, 1983. MR 0719020
- 9.
- -, Fundamentals of the Theory of Operator Algebras, vol. II, Academic Press, New York, 1986. MR 0859186
- 10.
- -, Fundamentals of the Theory of Operator Algebras, vol. III, Academic Press, New York, 1991. MR 1134132
- 11.
- -, Fundamentals of the Theory of Operator Algebras, vol. IV, Academic Press, New York, 1992. MR 1170351
- 12.
- Mackey, G. W., The Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, New York, 1963. MR 0155567
- 13.
- Murphy, G. J.,
-algebras and Operator Theory, Academic Press, Boston, 1990. MR 1074574
- 14.
- Wegge-Olsen, N. E.,
-theory and 
-algebras, Clarendon Press, Oxford Univ. Press, New York, 1993. MR 1222415
Review Information:
Reviewer:
William Arveson
Affiliation:
University of California, Berkeley
Email:
arveson@math.berkeley.edu
Journal:
Bull. Amer. Math. Soc.
34 (1997), 435-439
DOI:
https://doi.org/10.1090/S0273-0979-97-00729-5
Review copyright:
© Copyright 1997
American Mathematical Society
