In this talk I will construct the map between Algebraic and Topological K-Theory for Banach Algebras. We will complete this construction by following our Banach algebra through its general linear group construction, taking Milnor's classifying space, and then applying the plus construction. We will show that this construction agrees with the traditional definition of these K-Theories, while also returning maps between them.

The comparison map between Algebraic and Topological K-Theory for Banach Algebras