fa.functional analysis - Bibliography for topologies defined by a family of seminorms

I just had a look at

Topological Vector Spaces,
Distributions and Kernels

by Francois Treves. It is divided into three parts:

I Topological Vector Spaces. Spaces of Funtions

• covering: basic material about locally convex spaces and Frechet spaces (with a lot of examples)

II Duality, Spaces of Distributions

• topologies on Duals, transposes of linear maps, convolution, barreled spaces

III Tensor Products. Kernels

• injective and projective tensor products and their relation to bilinear forms, nuclear spaces, nuclear mappings, Schwartz kernel theorem and applications

From the first sight, this looks like a good place to start if you are already familiar with functional analysis on Banach and Hilbert spaces.