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Published online by Cambridge University Press: 10 February 2020
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.
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