This 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 Οℑp space (equivalently, a rigid Οℑ p space) if and only if it is a matrix orderly rigid Οℑp space (equivalently, a matrix orderly rigid Οℑp, 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.
ASJC Scopus subject areas