Infusino M. Topological Vector Spaces

University of Konstanz, 2017. — 81 p.The theory of topological vector spaces (TVS), as the name suggests, is a beautiful connection between topological and algebraic structures. Alexander Grothendieck is surely the name which is most associated to the theory of TVS. Of course great contributions to this theory were already given before him (e.g. the Banach and Hilbert spaces are examples of TVS), but Alexander Grothendieck was engaged in a completely general approach to the study of these spaces and collected some among the deepest results on TVS in his Phd thesis (1950-1953) written under the supervision of Jean Dieudonn´e and Laurent Schwartz. After his dissertation he said: “There is nothing more to do, the subject is dead”.
Despite this sentence come out of the mouth of a genius, the theory of TVS is far from being dead. Many aspects are in fact still unknown and the theory lively interacts with several interesting problems which are still currently unsolved!