4) The spaces "S""p"("H") of operators in the Schatten class on a Hilbert space "H" are uniformly convex, hence reflexive, when . When the dimension of "H" is infinite, then "S"1("H") (the trace class) is not reflexive, because it contains a subspace isomorphic to ℓ1, and "S"∞("H") = "L"("H") (the bounded linear operators on "H") is not reflexive, because it contains a subspace isomorphic to ℓ∞. In both cases, the subspace can be chosen to be the operators diagonal with respect to a given orthonormal basis of "H".