book recommendation on functional analysis

manpreet Best Answer 3 years ago

I recently started studying functional analysis. I have many ebooks loaded on my laptop, but can't figure out which one to start with. I've asked my instructor, and he says there aren't any specific books to start with. Here's a brief list of the topics on our syllabus:

1. Normed linear spaces
2. Banach Spaces
3. Hilbert spaces
4. Compact Operators
5. Knowledge of C[0,1],Lp[0,1]C[0,1],Lp[0,1]
6. Continuous linear operators
7. Hahn-Banach theorem
8. Open mapping and Closed Graph Theorem
9. Uniform Boundedness Principle

I'm seeing these topics first in my lifetime. One thing I want to ask is whether functional analysis is very difficult. Please suggest some books to start this topic which covers the above and contains some exercises. Thanks in advance.