I recently started functional analysis in more depth. I followed a standard course on functional analysis at the master's degree but clearly it was very basic and many results are deeper than the one it covered.
I'm looking for a book which starts from topological vector spaces and goes through to metric spaces, normed spaces, Banach spaces and Hilbert spaces. IN this sense [Rudin, Functional analysis] is surely the right book. Are there some simpler alternatives to Rudin's book with this structure so that I can read 2 or more books?
(Also [Yosida, Functional analysis] has this kind of structure but it is too advanced and very difficult to read for me).
Best Answer
Here is a classic that starts with topological vector spaces and works down. It's a Dover publication.
I think this is what you're looking for.