We study the local lifting property for operator spaces. This is a natural non-commutative analogue of the Banach space local lifting property, but is very different from the local lifting property studied in C~*-algebra theory. We show that an operator space has the #lambda#-local lifting property if and only if it is an L#GAMMA#_(1, #lambda#) space. These operator space are #lambda#-completely isomorphic to the operator subspaces of the operator preduals of von Neumann algebras, and thus #lambda#-locally reflexive. Moreover, we show that an operator space V has the #lambda#-local lifting property if and only if its operator space dual V~* is #lambda#-injective.
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