(Sorry for my bad English.)
For "applications", I mean applications in math, not real-life.
There are many textbooks about topological vector space, for example, GTM269 by Osborne, Modern Methods in Topological Vector Spaces by ALBERT WILANSKY, etc.
Most textbooks make many definitions, and proved many theorem of their properties, but with very few application.
For example, in GTM269 preface, the author says "Although this book is oriented toward applications, the beauty of the subject may appeal to you."
But most theorems in this book really don't have any application (in book).
So, are there some topological vector space textbook (about generally topological vector space, Frechet space, locally convex space or this kind of spaces. Not Banach space or Hilbert space), which most theorems have applications?