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.


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