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1 results

  • 9 - Nuclear pairs, WEP, LLP, QWEP

  • 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 180-209

  • Summary

    We describe the main properties of the bidual of a C*-algebra, that is also its enveloping von Neumann algebra. We define the tensor norms that naturally appear on a mixed pair formed of a C*-algebra and a von Neumann one, called the nor-norm and the bin-norm. This leads naturally to the notion of local reflexivity, which, in sharp contrast with the Banach space case, is not valid for all C*-algebras. Wegive explicit examples exhibiting that phenomenon, which is specific to the min-tensor product. Indeed, we show that the analogous defect disappears for the max-tensor product.