Pointwise bounded asymptotic morphisms and Thomsen's non-stable k-theory

TL;DR

This paper establishes a connection between pointwise bounded asymptotic morphisms and Thomsen's non-stable k-theory for certain *-algebras, showing how these morphisms induce continuous maps on quasi-unitary groups.

Contribution

It demonstrates that under specific conditions, asymptotic morphisms induce continuous maps on quasi-unitary groups, linking asymptotic morphisms to Thomsen's non-stable k-theory.

Findings

Asymptotic morphisms induce continuous maps between quasi-unitary groups.

A composition result for asymptotic morphisms is established.

The work connects asymptotic morphisms with Thomsen's non-stable k-theory.

Abstract

In this paper I show that pointwise bounded asymptotic morphisms between separable metrisable locally convex *-algebras induce continuous maps between the quasi-unitary groups of the algebras, provided that the algebras support a certain amount of functional calculus. This links the asymptotic morphisms directly to Thomsen's non-stable definition of k-theory in the C* algebra case. A result on composition of asymptotic morphisms is also given.