Calculus in Banach Spaces Reference Request Can anyone suggest a text that gives a complete/thorough treatment of calculus in Banach spaces? Perhaps something something along the lines of Chapter 2 in Manifolds, Tensor Analysis and Applications by Marsen, et. al. but more expansive?
Thanks.
 A: I studied it from Cartan's book: Differential Calculus. I found it a good exposition of the theory. That's my indication :)
A: The only one I know is Jean Dieudonne's classic Foundations of Modern Analysis, which is the also the most cited out of print text I know. It's kind of strange since in the late 1960's and early 1970's, at the height of the Bourbaki Era, it was the single most cited analysis text for undergraduates and was fully expected to replace Rudin as the gold standard.
Anyway,I think you'll find exactly what you want in that text-if you're ready for it. It's a tough read-get your pencil and paper ready when you go to read it! there's now  an inexpensive edition.  
A: Bourbaki's "Functions of one real variable" would do the job. It is quite expansive. You could even work in conjuction with with the Bourbaki volumes on Topology, and Topological vector spaces. But the pedagogical value is as always questionable.
Edit: If your aim is to learn analysis on Banach manifolds, then Serge Lang's book on differentiable manifolds is the answer. 
