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1 results

  • 16 - Equivalence with Tsirelson’s problem

  • Gilles Pisier, Texas A & M University
  • Book:
    Tensor Products of <I>C</I>*-Algebras and Operator Spaces
    Published online:
    10 February 2020
    Print publication:
    27 February 2020, pp 300-310

  • Summary

    We prove here that the Connes and Kirchberg questions are equivalent to a different longstanding conjecture that circulated among Banach space theorists at least since the 1980’s if not sooner, namely the finite representability problem. The latter asks whether the predual of any von Neumann algebra is finitely representable in the trace class, or equivalent whether it embeds isometrically in an ultrapower (in the Banach space sense) of the trace class.