Fubini's Theorem for Ultraproducts of Noncommutative L p -Spaces

Source abstract

Abstract Let (ℳ i ) i ∈ I , be families of von Neumann algebras and be ultrafilters in I , J , respectively. Let 1 ≤ p < ∞ and n ∈ ℕ. Let x 1 ,… , x n in Π L p (ℓ i ) and y 1 ,… , y n in be bounded families. We show the following equality For p = 1 this Fubini type result is related to the local reflexivity of duals of C *-algebras. This fails for p = ∞.