On injectivity and nuclearity for operator spaces

Abstract

An injective operator space $V$ which is dual as a Banach space has the form $eR(1-e)$, where $R$ is an injective von Neumann algebra and where $e$ is a projection in $R$. This is used to show that an operator space $V$ is nuclear if and only if it is locally reflexive and $V^{\ast\ast}$ is injective. It is also shown that any exact operator space is locally reflexive.