Extension of C*-bundles

TL;DR

This paper investigates the conditions under which various fibrewise amalgamated products of continuous C*-bundles remain continuous, unifying previous approaches within a common theoretical framework.

Contribution

It provides a comprehensive characterization of the continuity properties of amalgamated products of C(X)-algebras, integrating diverse methods in the theory.

Findings

Characterization of when amalgamated products are continuous C*-bundles

Unification of different approaches in the theory of C*-bundles

Framework for understanding deformation and amalgamation in C*-algebras

Abstract

Different (fibrewise) amalgamated products of continuous C*-bundles have been studied over the last years, one of the main question being to know when these amalgamated products are continuous C*-bundles. In order to gather these approaches in a joint framework, we first recall a few definitions from the theory of deformations of C*-algebras and we fix several notations that will be used in the sequel. Then we characterise the continuity properties of different amalgamated products of (continuous) C(X)-algebras.