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

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Kirchberg asked in 2004 whether the commutant of L(H) in its (norm) ultrapower is trivial. Assuming the Continuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, ON, M3J 1P3, Canada

    Ilijas Farah

  2. Matematicki Institut, Kneza Mihaila 34, Belgrade, Serbia

    Ilijas Farah

  3. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA

    N. Christopher Phillips

  4. Fields Institute, 222 College Street, Toronto, ON, Canada

    Juris Steprāns

Authors
  1. Ilijas Farah
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  2. N. Christopher Phillips
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  3. Juris Steprāns
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Corresponding author

Correspondence to Ilijas Farah.

Additional information

Ilijas Farah and Juris Steprāns were partially supported by NSERC. N. Christopher Phillips was partially supported by NSF grant DMS-0701076, by the Fields Institute for Research in Mathematical Sciences, Toronto, Canada, and by an Elliott Distinguished Visitorship at the Fields Institute.

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Farah, I., Phillips, N.C. & Steprāns, J. The commutant of L(H) in its ultrapower may or may not be trivial. Math. Ann. 347, 839–857 (2010). https://doi.org/10.1007/s00208-009-0448-z

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  • DOI: https://doi.org/10.1007/s00208-009-0448-z

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