Functional Analysis: Lax vs Reed/Simon?

Question

I am doing my MS in pure mathematics and I am aspiring to become a mathematical physics. I have some familiarity with functional analysis due to some courses that mentioned some of the major theorems and also by some reading here and there, but I never really focused on the subject on its own. I've noticed how important functional analysis is for mathematical physics and so I would like to learn it in detail on my own.

The two books I am thinking of using is Lax and Reed/Simon Vol I. The latter seems to be exactly what I want since it focuses on mathematical physics, but a few friends of mine have told me that Lax is an easier read with better exposition (and easier to understand proofs), covers more, and is more modern. What do you all think of these two books? Can anyone vouch for one book over another?

Answer 1

My memory is that they don’t overlap all that much. I prefer Lax, but the historical notes at the end of most chapters are so depressing.

Answer 2

Haven't studied functional analysis myself but Lax is one of the standard textbooks on the subject at the level of the first year grad school in the US. Barry Simon has a reputation of being quite hard core analysis from what I have seen.

Also Lax is an preeminent applied mathematician his text won't be 100% pure math if that's your concern.

Another 2 standard textbooks on the subject are written by John Conway Abstract Analysis (or something along these lines) and Functional Analysis. The former being the less advanced of the two.

Answer 3

Anyone have thoughts on Rudin?

Answer 4

Can't vouch for either, but you could also check out Linear Analysis by Bolobas, it's one of my favorite references.