Speaker
Description
On the one hand, the classical Banach-Stone theorem shows that the topological structure of a compact Hausdorff space $\Omega$ is determined by the geometry of $C(\Omega)$, the Banach space of continuous scalar-valued functions on $\Omega$, while on the other hand, it gives an explicit description of surjective linear isometries between two Banach spaces of continuous functions, $C(\Omega_1)$ and $C(\Omega_2)$. This theorem has been generalized in various ways. In this talk, following a long line of work on analogues of this classical theorem in the framework of $C^*$-algebras, we will arrive at a recent result of this type, without requiring that the isometries be linear or that the $C^*$-algebras be unital. This is a result from a joint work with C. Bénéteau, F. Botelho, M. Cueto Avellaneda, J. E. Guerra, S. Kazemi and S. Oi.
