Bivariant $K$-theory for locally convex algebras and the Chern-Connes character

Abstract

We present a new construction of a bivariant $K$-functor. The functor can be defined on various categories of topological algebras. The corresponding bivariant theory has a Kasparov product and the other standard properties of $KK$-theory. We study such a theory in detail on a natural category of locally convex algebras and define a bivariant multiplicative character to bivariant periodic cyclic cohomology.