Reddit reviews Functional Analysis (Methods of Modern Mathematical Physics (Volume 1))
We found 6 Reddit comments about Functional Analysis (Methods of Modern Mathematical Physics (Volume 1)). Here are the top ones, ranked by their Reddit score.
If that's what you value in a tofu press I might recommend
I like Kolmogorov as well.
You might try Reed and Simon which is aligned more closely to physics than to pure mathematics, but has all the rigor you would hope for.
I'm a big fan of
Strocchi's Introduction to the Mathematical Structure of Quantum Mechanics where the first couple of chapters give a very nice, concise introduction to (and derivation of!) the C*-algebraic background to quantum mechanics. If you really want to do things rigorously, you'll of course end up with the four volumes of Reed and Simon... of course, these sources are for quantum mechanics, not QFT per se, which is a different kettle of fish entirely.
If you want to carry on with the algebraic formalism in QFT you'll end up with local QFT which involves assigning an algebra of observables to regions of spacetime.
If you work with linear PDE (including perhaps the linearizations of some nonlinear PDE), you'll want to go deeper into spectral theory and functional calculus. The last few chapters of Reed and Simon is a good next step, and then you can down the rabbit hole into semigroup theory, spectral theory, spectral geometry, etc. But otherwise, that's probably enough functional analysis for whatever you want to study in nonlinear PDE.
I think Methods of Modern Mathematical Physics by Reed and Simon is the standard reference for this. Some other books I've seen recommended are Linear Operators in Hilbert Spaces by Weidmann and Unbounded Self-adjoint Operators on Hilbert Space by Schmüdgen.
Unfortunately I don't know of any good books firsthand - my knowledge comes from learning physics and then learning analysis =P
A great reference (albeit rather heavy for an intro) is Reed & Simon's Functional Analysis, first in a 4-part series. Volumes 2 and 4 look like they would be more physics-oriented, though I haven't read them myself.