functions from real to banach space

[singhal...@gmail.com]

Hi all,

I am doing research in function spaces.
I have two questions_

1. i am stuck in the function of type----------
Let U be a domain in R^n and X be a Banach space then i want to study
about C^k(U,X) , k times continuous differentiable functions.
Can U suggest me some book for studing it?

2. if g is mollifier from U to R^n and f : U ---> X, X is a banach
space then wheather gf will be infinitly continuous differentiable
function from U to R^n?