Functional Analysis and Applications Seminar 

20/10/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Lina Oliveira, Instituto Superior Técnico, U.T. Lisboa

A non-commutative notion of topology

The Gelfand-Naimark theorem establishes that any commutative $C^{*}$-algebra $A$ is isometrically $*$-isomorphic to a certain space of continuous functions over a locally compact topological space. In a way, the $C^{*}$-algebra $A$ might be seen as a translation of the topology of the space. It is the aim of this talk to give an overview of how the generalization of these ideas to non-commutative $C^{*}$-algebras has lead to a non-commutative notion of topology. A résumé of some recent results and of on going research will be presented.