Banach embedding properties of non-commutative L^p-spaces

U. Haagerup, H. P. Rosenthal, F. A. Sukochev

Let N and M be von Neumann algebras. It is proved that L^p(N) does not Banach embed in L^p(M) for N infinite, M finite, 1 < or = p < 2. The following considerably stronger result i…