Archive for Mathematical Logic

, Volume 52, Issue 5–6, pp 517–524 | Cite as

Some Calkin algebras have outer automorphisms



We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, assuming some restriction of the Generalized Continuum Hypothesis, there are many outer automorphisms.


Calkin algebra Nonseparable Continuum Hypothesis 

Mathematics Subject Classification (2000)

03E75 46L40 


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  1. 1.
    Farah I.: All automorphisms of all Calkin algebras. Math. Res. Lett. 18(3), 489–503 (2011)MathSciNetMATHGoogle Scholar
  2. 2.
    Farah, I. All automorphisms of the Calkin algebra are inner. Ann. Math. 173(2), 619–661 (2011). doi: 10.4007/annals.2011.173.2.1 Google Scholar
  3. 3.
    Moore, J.T.:(2010) The proper forcing axiom. In: Proceedings of the International Congress of Mathematicians, vol. II, pp. 3-29. Hindustan Book Agency, New DelhiGoogle Scholar
  4. 4.
    Phillips, N.C., Weaver, N.: The Calkin algebra has outer automorphisms. Duke Math. J. 139(1), 185–202 (2007). doi: 10.1215/S0012-7094-07-13915-2
  5. 5.
    Rudin W.: Homogeneity problems in the theory of Čech compactifications. Duke Math. J. 23, 409–419 (1956)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Shelah S.: Proper forcing, Lecture Notes in Mathematics, vol. 940. Springer, Berlin (1982)CrossRefGoogle Scholar
  7. 7.
    Shelah, S., Steprāns, J.: PFA implies all automorphisms are trivial. Proc. Am. Math. Soc. 104(4), 1220–1225 (1988). doi: 10.2307/2047617
  8. 8.
    Veličković, B.: OCA and automorphisms of \({\mathcal{P}(\omega)/\mathrm{fin}}\), Topol. Appl. 49(1), 1–13 (1993). MR1202874 (94a:03080)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ilijas Farah
    • 1
    • 2
  • Paul McKenney
    • 3
  • Ernest Schimmerling
    • 3
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada
  2. 2.Matematicki InstitutBelgradeSerbia
  3. 3.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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