**"****Noncommutative Hahn-Banach Type Theorems****"**

By

**SERDAR AY**

**(BİLKENT UNIVERSITY)**

**Abstract: ** 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.

**Date: ****Tuesday, September 30, 2014**

**Time: ****15:40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.