Set theory and C*-algebras

Bulletin of Symbolic Logic

Volumn 13, Issue 1, 2007, Pages 1-20

  Weaver, Nik ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947544817     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2178/bsl/1174668215     Document Type: Review

References (62)

1. C. AKEMANN and N. WEAVER, Consistency of a counterexample to Naimark's problem, Proceedings of the National Academy of Sciences of the United States of America, vol. 101 (2004), pp. 7522-7525.
2. C. A. AKEMANN, J. ANDERSON, and G. K. PEDERSEN, Diffuse sequences and perfect C*-algebras, Transactions of the American Mathematical Society, vol. 298 (1986), pp. 747-762.
3. _, Excising states of C*-algebras, Canadian Journal of Mathematics, vol. 38 (1986), pp. 1239-1260.
4. C. A. AKEMANN and G. K. PEDERSEN, Ideal perturbations of elements in C*-algebras, Mathematica Scandinavica, vol. 41 (1977), pp. 117-139.
5. C. A. AKEMANN and F. W. SHULTZ, Perfect C*-algebras, vol. 55, Memoirs of the American Mathematical Society, no. 326, 1985.
6. S. ALBEVERIO, D. GUIDO, A. PONOSOV, and S. SCARLATTI, Singular traces and compact operators, Journal of Functional Analysis, vol. 137 (1996), pp. 281-302.
7. J. ANDERSON, A maximal abelian subalgebra of the Calkin algebra with the extension property, Mathematica Scandinavica, vol. 42 (1978), pp. 101-110.
8. _, Extensions, restrictions, and representations of states on C*-algebras, Transactions of the American Mathematical Society, vol. 249 (1979), pp. 303-329.
9. _, Extreme points in sets of positive linear maps on B(H), Journal of Functional Analysis, vol. 31 (1979), pp. 195-217.
10. _, Pathology in the Calkin algebra. Journal of Operator Theory, vol. 2 (1979). pp. 159-167.
11. _, A conjecture concerning the pure states of B(H) and a related theorem, pp. 27-43, Birkhaüser, 1981, pp. 27-43.
12. H. ARAKI, Mathematical theory of quantum fields, Oxford University Press, 1999.
13. R. ARCHBOLD, On perfect C*-algebras. Proceedings of the American Mathematical Society, vol. 97 (1986), pp. 413-417.
14. B. E. BLACKADAR, Weak expectations and nuclear C*-algebras, Indiana University Mathematics Journal, vol. 27 (1978), pp. 1021-1026.
15. A. BLASS, Near coherence of filters II: applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups, Transactions of the American Mathematical Society, vol. 300 (1987), pp. 557-581.
16. A. BLASS and S. SHELAH, Near coherence of filters III: a simplified consistency proof, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 530-538.
17. A. BLASS and G. WEISS, A characterization and sum decomposition for operator ideals, Transactions of the American Mathematical Society, vol. 246 (1978), pp. 407-417.
18. O. BRATTELI and D. W. ROBINSON, Operator algebras and quantum statistical methanics 2: Equilibrium states, models in quantum statistical mechanics, second ed., Springer-Verlag, 1997.
19. P. G. CASAZZA and J. C. TREMAIN, The Kadison Singer problem in mathematics and engineering, Proceedings of the National Academy of Sciences of the United States of America, vol. 103 (2006), pp. 2032-2039.
20. A. CONNES, A survey of foliations and operator algebras, Operator algebras and applications, Part I, American Mathematical Society, 1982, pp. 521-628.
21. J. B. CONWAY, A course in functional analysis, second ed., Springer-Verlag, 1990.
22. H. G. DALES and W. H. WOODIN, An introduction to independence for analysts, Cambridge University Press, 1987.
23. K. R. DAVIDSON, Similarity and compact perturbations of nest algebras, Journal für die Reine und Angewandte Mathematik, vol. 348 (1984), pp. 72-87.
24. J. DIXMIER, Anneaux d'opérateurs et représentations des groupes. Séminaire Bourbaki, vol. 1 Exp. No. 40, Société Mathématique de France, 1995, pp. 331-336.
25. A. DOW, On ultrapowers of Boolean algebras. Topology Proceedings, vol. 9 (1984), pp. 269-291.
26. 0, Proceedings of the American Mathematical Society, vol. 112 (1991), pp. 949-957.
27. L. GE and D. HADWIN, Ultraproducts of C*-algebras, Recent advances in operator theory and related topics (L. Kerchy et al., editors), Operator Theory: Advances and Applications, vol. 127, pp. 305-326.
28. J. GLIMM, Type I C*-algebras, Annals of Mathematics, vol. 73 (1961), pp. 572-612.
29. D. HADWIN, Maximal nests in the Calkin algebra, Proceedings of the American Mathematical Society, vol. 126 (1998), pp. 1109-1113.
30. L. A. HARRINOTON, A. S. KECHRIS, and A. LOUVEAU, A Glimm-Effros dichotomy for Borel equivalence relations. Journal of the American Mathematical Society, vol. 3 (1990), pp. 903-928.
31. 1, Illinois Journal of Mathematics, vol. 37 (1993), pp. 1-13.
32. T. HURUYA, Decompositions of linear maps into nonseparable C*-algebras, Kyoto University. Research Institute for Mathematical Sciences. Publications, vol. 21 (1985), pp. 645-655.
33. T. JECH, Set theory, Springer-Verlag, 2003.
34. B. E. JOHNSON and S. K. PARROTT, Operators commuting with a von Neumann algebra modulo the set of compact operators. Journal of Functional Analysis, vol. 11 (1972), pp. 39-61.
35. V. F. R. JONES, Subfactors and knots, American Mathematical Society, 1991.
36. P. E. T. JORGENSEN, Analysis and probability: Wavelets, signals, fractals, Springer-Verlag, 2006.
37. R. V. KADISON and J. R. RINGROSE, Fundamentals of the theory of operator algebras, vol. I, American Mathematical Socitey, 1997.
38. R. V. KADISON and I. M. SINGER, Extensions of pure states, American Journal of Mathematics, vol. 81 (1959), pp. 383-400.
39. G. G. KASPAROV, Equivariant KK-theory and the Novikov conjecture, Inventiones Mathematicae, vol. 91 (1988), pp. 147-201.
40. K. KUNEN, Set theory: An introduction to independence proofs, North-Holland, 1980.
41. K. B. LAURSEN, Continuity of homomorphisms from C*-algebras into commutative Banach algebras, Journal of the London Mathematical Society, vol. 36 (1987), pp. 165-175.
42. R. D. MAULDIN, A representation theorem for the second dual of C[0,1], Studia Mathematica, vol. 46 (1973), pp. 197-200.
43. D. MUNDICI, Simple Bratteli diagrams with a Gödel-incomplete C*-equivalence problem, Transactions of the American Mathematical Society, vol. 356 (2004), pp. 1937-1955.
44. M. A. NAIMARK, Rings with involutions, Uspehi Matematiceskih Nauk (N.S.), vol. 3 (1948), pp. 52-145, Russian.
45. _, On a problem of the theory of rings with involution, Uspehi Matematiceskih Nauk (N.S.), vol. 6 (1951), pp. 160-164, Russian.
46. G. K. PEDERSEN, C*-algebras and their automorphism groups, Academic Press, 1979.
47. G. A. REID, On the Calkin representations, Proceedings of the London Mathematical Society, vol. 23 (1971), pp. 547-564.
48. A. ROSENBERG, The number of irreducible representations of simple rings with no minimal ideals, American Journal of Mathematics, vol. 75 (1953), pp. 523-530.
49. V. RUNDE, The structure of discontinuous homomorphisms from non-commutative C*-algebras, Glasgow Mathematical Journal, vol. 36 (1994), pp. 209-218.
50. S. SAKAI, C*-algebras and W*-algebras, Springer-Verlag, 1971.
51. S. SHELAH, Proper forcing, Springer-Verlag, 1982.
52. _, Classification theory and the number of nonisomorphic models, North-Holland, 1990.
53. S. SHELAH and J. STEPRĀNS, PFA implies all automorphisms are trivial, Proceedings of the American Mathematical Society, vol. 104 (1988), pp. 1220-1225.
54. M. TAKESAKI, Theory of operator algebras I, Springer-Verlag, 1979.
55. J. VAN MILL, An introduction to βω, Handbook of set-theoretic topology (K. Kunen and J. Vaughan, editors), North-Holland, 1984, pp. 503-567.
56. B. VELIČKOVIĆ, OCA and automorphisms of P(ω)/fin, Topology audits Applications, vol. 49 (1993), pp. 1-13.
57. J. VESTERSTRØM, Quotients of finite W*-algebras, Journal of Functional Analysis, vol. 9 (1972), pp. 322-335.
58. R. M. WALD, Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, 1994.
59. N. WEAVER, Mathematical quantization, CRC Press, 2001.
60. _, A prime C*-algebra that is not primitive. Journal of functional Analysis. vol. 203 (2003), pp. 356-361.
61. _, The Kadison-Singer problem in discrepancy theory, Discrete Mathematics, vol. 278 (2004), pp. 227-239.
62. E. WOFSEY, Set theory and projections in the Calkin algebra, manuscript.