Reference for projective limits of Banach Spaces..

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I have just started studying a book about pseudo-differential operators and I came across projective limits of Banach spaces and I got lost. I have never studied this, so can anyone recommend me some nice references to get started to it?

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These notes by Taylor discuss this particular construction.

More generally, this falls into the very deep, rich theory of locally convex topological vector spaces. Good places to start include the book Topological Vector Spaces, Distributions and Kernels by Treves as well as early works by Grothendieck (in particular, his book Topological Vector Spaces or Bourbaki's book of the same title).