Fubini's theorem for ultraproducts of noncommutative Lp-spaces

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Let (Mi)i ∈ I, (Nj) j ∈ J be families of von Neumann algebras and U, U′ be ultrafilters in I, J, respectively. Let 1 ≤ p < ∞ and n ∈ ℕ. Let x1,...,xn in ∏ Lp (M i) and y1,...,yn in ∏ Lp (Nj) be bounded families. We show the following equality (Equation presented) For p = 1 this Fubini type result is related to the local reflexivity of duals of C*-algebras. This fails for p = ∞.

Original languageEnglish (US)
Pages (from-to)983-1021
Number of pages39
JournalCanadian Journal of Mathematics
Issue number5
StatePublished - Oct 2004


  • Noncommutative L-spaces
  • Ultraproducts

ASJC Scopus subject areas

  • General Mathematics


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