I will be studying Functional Analysis for the first time, at the first-year grad school level. My relevant background is $1$ basic course in Topology and $1$ basic course in Measure Theory.
I was given some recommendations for what textbooks may be suitable to a person in my position (sufficient detail to learn at the graduate level, but easy enough for a complete beginner to hit the ground running), and I now have to make a decision that will haunt me for a semester. My question is Based on your experience, can you give me any insight into the pros and cons of any of these books:
- W. Rudin, Functional Analysis
- G.K. Pedersen, Analysis Now
- R.J. Zimmer, Essential results of functional analysis
- J.B. Conway, A course in functional analysis
- C.D. Aliprantis, K. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide (a comprehensive text, but don't feel intimidated)
- B. Simon, Convexity: An analytic approach (as you can guess by the title, not exactly what we are doing but this text is an excellent supplement)