Abstract. In this talk I will present joint work with Bruno M. Braga, continuing the study of the nonlinear geometry of operator spaces that was recently started by Braga and Sinclair.
Operator spaces are Banach spaces with an extra "noncommutative" structure. Their theory sometimes resembles very closely the Banach space case, but other times is very different. Our main result is an instance of the latter: a completely coarse map between operator spaces (that is, a map such that the sequence of its amplifications is equi-coarse) has to be real-linear.