Two results on Fréchet Schwartz spaces (Q1312348)

Two results on Fréchet-Schwartz spaces are proved. (1) Every Fréchet-Schwartz space is isomorphic to a quotient of a Köthe-Schwartz space of type \(\lambda^ 1(A)\). (2) Every countably normed Fréchet-Schwartz space is isomorphic to a (closed) subspace of a Köthe-Schwartz space of type \(\lambda^ \infty(A)\) with a continuous norm. The proofs are ingenious ad hoc constructions relying on the well-known representation of precompact subsets of metrizable locally convex spaces by infinite absolutely convex combinations of sequences converging to zero.