The Predual of a Type I Von Neumann Algebra

Abstract

A von Neumann algebra A on a separable, complex Hilbert space H has property A n if for every n × n array {f i , j } of elements in the predual there exist sequences {x i }, {y j } in H such that f i , j (a) = (ax i , y j ) for all a in A and 0 ≤ i, j < n. We characterize the type I von Neumann algebras with property A n .