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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
A good book of functional analysis
Let me add to this list of suggestions the nice and recent book by J. Cerda "Linear Functional Analysis", Graduate Studies in Mathematics, Vol. 116, AMS-RSME, 2010.
-1
votes
Sufficient criteria for $X \subset \mathcal{H}$ to be a Lipschitz (or unif. cont.) retract o...
I think what you are looking for is Kirszbraun theorem: https://en.wikipedia.org/wiki/Kirszbraun_theorem