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Book Review

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Book Information:

Author: Ola Bratteli
Title: Derivations, dissipations and group actions on $C^ *$-algebras
Additional book information: Lecture Notes in Mathematics, vol. 1229, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1986, vi + 277 pp., $23.60. ISBN 0-387-17199-1.

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

  • 1. Charles A. Akemann and Gert K. Pedersen, Central sequences and inner derivations of separable 𝐶*-algebras, Amer. J. Math. 101 (1979), no. 5, 1047–1061. MR 546302, https://doi.org/10.2307/2374125
  • 2. B. Blackadar, Operator algebras, Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, Berlin, 2006. Theory of 𝐶*-algebras and von Neumann algebras; Operator Algebras and Non-commutative Geometry, III. MR 2188261
  • 3. Ola Bratteli, George A. Elliott, and Palle E. T. Jorgensen, Decomposition of unbounded derivations into invariant and approximately inner parts, J. Reine Angew. Math. 346 (1984), 166–193. MR 727402
  • 4. Alain Connes, 𝐶* algèbres et géométrie différentielle, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 13, A599–A604 (French, with English summary). MR 572645
    Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
  • 7. J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, 2nd ed., Gauthier-Villars, Paris, 1969.
  • 8. G. A. Elliott, Some C*-algebras with outer derivations. III, Ann. of Math. (2) 106 (1977), 121-143. MR 448093
  • 9. Palle E. T. Jorgensen and Robert T. Moore, Operator commutation relations, Mathematics and its Applications, D. Reidel Publishing Co., Dordrecht, 1984. Commutation relations for operators, semigroups, and resolvents with applications to mathematical physics and representations of Lie groups. MR 746138
    Paul S. Muhly (ed.), Operator algebras and mathematical physics, Contemporary Mathematics, vol. 62, American Mathematical Society, Providence, RI, 1987. MR 878371
    Richard V. Kadison, Operator algebras—the first forty years, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 1–18. MR 679692
    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
  • 13. I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-859. MR 58137
  • 14. T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1976. MR 407617
  • 15. D. Montgomery and L. Zippin, Topological transformation groups, Interscience Publishers, Inc., New York, 1955. MR 73104
  • 16. R. T. Powers, Resistance inequalities for KMS-states of the isotropic Heisenberg model, Comm. Math. Phys. 51 (1976), 151-156. MR 426743
  • 17. R. T. Powers and S. Sakai, Existence of ground states and KMS states for approximately inner dynamics, Comm. Math. Phys. 39 (1975), 273-288. MR 359623
  • 18. Marc A. Rieffel, 𝐶*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), no. 2, 415–429. MR 623572
  • 20. I. E. Segal, Notes towards the construction of nonlinear relativistic quantum fields. III, Properties of the C*-dynamics for a certain class of interactions, Bull. Amer. Math. Soc. 75 (1969), 1390-1395. MR 251992
  • 21. Ja. G. Sinaĭ and A. Ja. Helmskiĭ, A description of differentiations in algebras of the type of local observables of spin systems, Funktsional Anal. i Prilozhen 6 (1972), 99-100; English transl., Funct. Anal. Appl. 6 (1973), 343-344. MR 317686
  • 22. Hiroshi Takai, On a problem of Sakai in unbounded derivations, J. Funct. Anal. 43 (1981), no. 2, 202–208. MR 633976, https://doi.org/10.1016/0022-1236(81)90029-X
  • 23. C. -T. Yang, Hilbert's fifth problem and related problems on transformation groups, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R. I., 1976, pp. 142-146. MR 425999

Review Information:

Reviewer: Palle E. T. Jorgensen
Journal: Bull. Amer. Math. Soc. 17 (1987), 202-209
DOI: https://doi.org/10.1090/S0273-0979-1987-15565-0
American Mathematical Society