I am busy studying Banach algebras and really enjoy the theorems and results that I have worked through so far.
This got me wondering - what significance has the study of Banach algebras brought to other topics within Mathematics, i.e. interesting results, significant simplification of proofs etc?
Can anyone please tell me a few of these results (and perhaps give a possible reference), as I would really like to read into them further. I have heard that Banach algebras have specific beautiful applications in the theory of Fourier Analysis, but what results within the field did it bring to surface?