Jeff did not mention the excellent very categorical lectures given on operator spaces by Matthias Neufang at the FIELDS INSTITUTE Summer School in Operator Algebras held last summer at the University of Ottawa and that we both attended. I do not know if any version of Matthias' notes is available. The theme of tensor products was important. Not only did his lectures provide good motivation for studying the subject from a categorical viewpoint. He did not do the category theory of operator spaces but rather was explicitly conscious of the categorical content of what he was saying. His notes may be of some interest to others so let us hope he will put some of the material on the web. Tim Quoting Jeff Egger <jeffegger@yahoo.ca>:
Dear Andrej,
Conventional functional analysis is largely concerned with Banach spaces, and there's certainly alot that can be said about the category of Banach spaces and linear contractions (i.e., continuous linear transformations with norm less-than-or-equal-to 1).