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Published online by Cambridge University Press: 10 February 2020
One of Kirchberg’s conjecture that we emphasize here is whether the LLP implies the WEP. This actually reduces to the case of the full C* algebra C of the free group with countably infinitely many generators, which is the prototypical example with the LLP. The question is shown to be equivalent to a very simple inequality, involving the linear span of the unitary generators of C, that seems to be related to Grothendieck’s classicalinequality from Banach space theory. Various results are proved that tend to « almost prove » the conjecture, notably one by Tsirelson in which it would suffice to replace real scalars by complex ones to obtain the full conjecture.
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