Two results on Fr�chet Schwartz spaces
Copyright policy )Two results on Fr�chet Schwartz spaces
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.
- University of Wuppertal Germany
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Köthe-Schwartz space, countably normed Fréchet-Schwartz space, continuous norm, infinite absolutely convex combinations of sequences converging to zero, representation of precompact subsets of metrizable locally convex spaces, Sequence spaces (including Köthe sequence spaces)
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Köthe-Schwartz space, countably normed Fréchet-Schwartz space, continuous norm, infinite absolutely convex combinations of sequences converging to zero, representation of precompact subsets of metrizable locally convex spaces, Sequence spaces (including Köthe sequence spaces)
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