Hello
I am trying to learn more about Fréchet spaces (in order to study the theory of distributions) and was wondering what people thought was the best resource.
Thank you very much.
Hello I am trying to learn more about Fréchet spaces (in order to study the theory of distributions) and was wondering what people thought was the best resource. Thank you very much. 


I don't know much about distributions but if you're entering this area with such a motivation, maybe you could use Horvath's book "Topological vector spaces and distributions". The first part is a fine introduction to locally convex space theory in itself, and the presentation of this (rather standard) material should be convenient for anybody interested on the final chapter  distributions. By the way, a linear topology on a vector space which is defined using a family of seminorms is in general a locally convex topology, not necessarily metrizable (Fréchet spaces are metrizable and complete locally convex spaces). 


I just had a look at
by Francois Treves. It is divided into three parts: I Topological Vector Spaces. Spaces of Funtions
II Duality, Spaces of Distributions
III Tensor Products. Kernels
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. 

