Rigid OL_pstructures of non-commutative L_p-spaces associated with hyperfinite von Neumann algebras - Junge, Marius; Ruan, Zhong-Jin; Xu, Quanhua (MATHEMATICA SCANDINAVICA, 2005)
This paper is devoted to the study of rigid local operator space structures on non-commutative L_p-spaces. We show that for 1p eq 2 < ∞, a non-commutative L_p-space L_p(M) is a rigid OL_p space (equivalently, a rigid COL_p space) if and only if it is a matrix orderly rigid OL_p space (equivalently, a matrix orderly rigid COL_p space). We also show that L_p(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 L_p-spaces characterize hyperfinite von Neumann algebras.