turkmath.org

A subspace of a unital C^*-algebra which is closed under the involution * and containing the identity element is called an operator system. Arveson's Extension Theorem states that a completely positive map with domain an operator system and codomain B(H), extends to a completely positive map on the whole C^*-algebra, where B(H) is the C^*-algebra of all linear bounded operators on a Hilbert space H. This will be an introductory talk on the theorem, its proof and consequences. If time permits, we also talk about Wittstock's Extension Theorem, which is an analogue of Arveson's Extension Theorem for completely bounded maps.