Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
I'm looking for a book on functional analysis that would suit someone who is more algebraically/geometrically oriented and seeks to learn the subject with the goal of using it later for geometric analysis and/or topological k-theory (and maybe noncommutative geometry in the far future).
What would be a good book fitting this description?
I have the relevant background in basic measure theory, complex analysis and linear algebra.
I believe that
A. Ya. Helemskii, Lectures and Exercises on Functional Analysis, Translations of Mathematical Monographs , vol. 233 (2006).
in conjunction with some standard book such as
G. K. Pedersen, Analysis Now, Springer-Verlag, (1989).
should suit you well. Note that Pedersen's book itself contains lots of basic information about Banach and operator algebras which is probably what you need.
I think to prepare Geometrical Analysis the book of Abraham, Marsden and Ratiu Manifolds, Tensor Analysis and Applications is quite useful. And maybe Dieudonné is a good author to look at. He is from the so called Bourbaki group which tried to formulate known results in a most abstract way. It is called Éléments d’Analyse or similar.
