Resumen de Rigid OL~p structures of non-commutative L~p-spaces associated with hyperfinite von Neumann algebras

Z.-J. Ruan, Marius Junge

• his paper is devoted to the study of rigid local operator space structures on non-commutative Lp-spaces. We show that for 1≤p≠2<∞, a non-commutative Lp-space Lp(M) is a rigid OLp space (equivalently, a rigid COLp space) if and only if it is a matrix orderly rigid OLp space (equivalently, a matrix orderly rigid COLp space). We also show that Lp(M) has these local properties if and only if the associated von Neumann algebra M is hyperfinite. Therefore, these local operator space properties on non-commutative Lp-spaces characterize hyperfinite von Neumann algebras.