A note on Kasparov products

TL;DR

This paper presents a simplified construction of the Kasparov product by integrating Voiculescu's theorem and Cuntz's description of KK-theory, aiming to extend the approach to locally convex algebras.

Contribution

It introduces a straightforward method for constructing the Kasparov product, facilitating its application to more general algebraic contexts.

Findings

Simplified construction of Kasparov product

Extension to locally convex algebras

Potential for broader applications in KK-theory

Abstract

Combining Kasparov's theorem of Voiculesu and Cuntz's description of $KK$-theory in terms of quasihomomorphisms, we give a simple construction of the Kasparov product. This will be used in a more general context of locally convex algebras in order to treat products of certain universal cycles.