Re: How to motivate a student of functional analysis

A student interested in functional analysis presumably knows some about topological vector spaces in general and Mackey spaces in particular. He might be interested in knowing that the full subcategory of Mackey spaces has a *-autonomous structure. This means that if M and N are Mackey there is a topology on the vector space of continuous linear maps M --> N that makes it into a Mackey space, often denoted M -o N, and that if you let M* = M -o C, then the canonical map M --> M** is an isomorphism. There is also a tensor product @ and the usual isomorphism Hom(M@N,P) = Hom(M,N-oP). See M. Barr, On $*$-autonomous categories of topological vector spaces. \cahiers {41} (2000), 243--254.