Locally convex spaces and seminorms

Question

It is well known that locally convex spaces are both characterized as vector spaces in which the topology is determined by a family of seminorms as well as topological vector spaces having a 0-neighbourhood base of (absolutely) convex sets.

Most texts on locally convex spaces heavily use (absolutely) convex subsets in the development of the theory. In fact, one could make a dictionary translating a concept about seminorms to one about absolutely convex subsets (using the Minkowski functional of the absolutely convex set), and vice versa.

Does there exist a text which develops the theory of locally convex spaces mainly using seminorms, downplaying the use of (absolutely) convex sets?

Does there exist a text which develops the above-mentioned dictionary (beyond showing the equivalence between both definitions of locally convex space)?

Answer 1

Such a text is

Garnir, Henri G.; De Wilde, Marc; Schmets, Jean: Analyse fonctionnelle : Théorie constructive des espaces linéaires à semi-normes Tome 1, Théorie générale, Birkhäuser Verlag 1968

Answer 2

In Helemskii's book Lectures and Exercises on Functional Analysis chapter 4 is called Polynormed Spaces, Weak Topology, and Generalized Functions. It develops some of the classical theory of locally convex spaces with a strong emphasis on seminorms (or, as he calls them, prenorms -- which might be a better notion if you compare with, e.g., semi-continuity) and aspects of category theory.