Dear all, The next Banach spaces webinar is on Friday July 17 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Alejandro Chávez-Domínguez (University of Oklahoma) Title: Completely coarse maps are real-linear 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. Continuing the search for an “appropriate” framework for a theory of the nonlinear geometry of operator spaces, we introduce a weaker notion of embeddability between them and show that it is strong enough for some applications. For instance, we show that if an infinite dimensional operator space X embeds in this weaker sense into Pisier's operator Hilbert space OH, then X must be completely isomorphic to OH. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 24: Florent Baudier (TAMU) Thank you, and best regards, Bunyamin Sari