The commutant of L(H) in its ultrapower may or may not be trivial

Mathematische Annalen

Volumn 347, Issue 4, 2010, Pages 839-857

  Farah, Ilijas ^a,b   Phillips, N Christopher ^c   Steprans, Juris ^d  

^a YORK UNIVERSITY   (Canada)

^b MATHEMATICAL INSTITUTE   (Serbia)

^c UNIVERSITY OF OREGON   (United States)

^d FIELDS INSTITUTE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952880130     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-009-0448-z     Document Type: Article

References (26)

1. Blass, A.: Combinatorial cardinal characteristics of the continuum. In: Foreman, M., Magidor, M., Kanamori, A. (eds.) Handbook of Set Theory, Available at http://www.math.lsa.umich.edu/~ablass/set.html.
2. Ben Yaacov, I., Berenstein, A., Henson, C. W., Usvyatsov, A.: Model theory for metric structures. In: Chatzidakis, Z. et al. (eds.) Model Theory with Applications to Algebra and Analysis, vol. II. Lecture Notes series of the London Math. Society, no. 350. Cambridge University Press, pp. 315-427 (2008).
3. Connes A.: Outer conjugacy classes of automorphisms of factors. Ann. Sci. Éc. Norm. Sup. Sér. 4(8), 383-420 (1975).
4. Dixmier J.: Von Neumann Algebras. North-Holland, Amsterdam (1981).
5. Farah, I.: All automorphisms of the Calkin algebra are inner. preprint (arXiv: 0705. 3085v7 [math. OA]).
6. Farah I.: Semiselective coideals. Mathematika 45, 79-103 (1998).
7. Farah I.: The relative commutant of separable C*-algebras of real rank zero. J. Funct. Anal. 256, 3841-3846 (2009).
8. Farah, I., Hart, B., Sherman, D.: Model theory of operator algebras I: stability. preprint (arXiv: 0908. 2790v1 [math. OA]).
9. Farah, I., Hart, B., Sherman, D.: Model theory of operator algebras II: model theory (2009, in preparation).
10. Farah, I., Steprāns, J.: Flat ultrafilters (2009, in preparation).
11. Ge, L., Hadwin, D.: Ultraproducts of C*-algebras. Recent advances in operator theory and related topics (Szeged, 1999), Oper. Theory Adv. Appl. vol. 127. Birkhäuser, Basel, pp. 305-326 (2001).
12. Izumi M.: Finite group actions on C*-algebras with the Rohlin property. I. Duke Math. J. 122, 233-280 (2004).
13. 1 factor. Mem. Am. Math. Soc. 28, 237 (1980).
14. Kirchberg, E.: The classification of purely infinite C*-algebras using Kasparov's theory. preliminary preprint (3rd draft).
15. Kirchberg, E.: Central sequences in C*-algebras and strongly purely infinite algebras. Operator algebras: the Abel Symposium 2004, Abel Symp., vol. 1, Springer, Berlin, pp. 175-231 (2006).
16. 2. J. Reine Angew. Math. 525, 17-53 (2000).
17. Kunen K.: Some points in β N. Math. Proc. Cambridge Philos. Soc. 80(3), 385-398 (1976).
18. Kunen K.: Set Theory: An Introduction to Independence Proofs. North-Holland, Amsterdam (1980).
19. Mathias A. R. D.: Happy families. Ann. Math. Logic 12, 59-111 (1977).
20. McDuff D.: Central sequences and the hyperfinite factor. Proc. Lond. Math. Soc. 21, 443-461 (1970).
21. Ocneanu, A.: Actions of Discrete Amenable Groups on von Neumann Algebras. Springer-Verlag Lecture Notes in Math. no. 1138. Springer, Berlin (1985).
22. Phillips N. C.: A classification theorem for nuclear purely infinite simple C*-algebras. Documenta Math. 5, 49-114 (2000) (electronic).
23. Phillips N. C., Weaver N. C.: The Calkin algebra has outer automorphisms. Duke Math. J. 139, 185-202 (2007).
24. Shelah, S.: Proper and Improper Forcing, 2nd edn. Perspectives in Mathematical Logic, Springer, Berlin (1998).
25. Sherman, D.: Divisible operators in von Neumann algebras. Illinois J. Math. (in press).
26. Takesaki M.: Theory of Operator Algebras III. Springer, Berlin (2003).