Context: The category of Banach spaces, with the projective tensor product is a closed monoidal category.
Question 1: Is there a tensor product on the category of complete topological vector spaces, such that the monoidal stucture is closed?
Question 2: what are the "natural/nice" topologies to put on the set of continuous linear maps between two ctvs?
Question 3: Is it different if instead we use Fréchet (or nuclear Fréchet) spaces?