 
Summary: UNIVERSITY OF REGINA
Department of Mathematics and Statistics
Colloquium
Speaker: D Farenick
Date: 07 October 2005
Time: 3.30 o'clock
Location: College West 307.18 (Math & Stats Lounge)
Title: Type I injective envelopes of C
algebras
Abstract: The HahnBanach Extension Theorem in classical functional analysis asserts
that every continuous linear map of a subspace M of a complex Banach space X into
C has a continuous, linear extension to X such that = . It is very natural
to consider generalisations of the HahnBanach Theorem whereby the base field C is
replaced by some other higherdimensional structure. Operator systems have proved to
be a fruitful context in which to examine extension theory.
An operator system is a closed, unital, selfadjoint linear submanifold of a unital C

algbera. An operator system I is injective if for every inclusion E F of operator systems
each completely positive linear map : E I has a completely positive extension to
F. An injective envelope of an operator system E is an injective operator system I such
