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Characterization of the subspaces of (s) in the tame category. (English) Zbl 0663.46003
This article contains a complete characterization of all graded Fréchet spaces, i.e. Fréchet spaces equipped with a fixed fundamental system of seminorms, which are tamely isomorphic to a subspace of s, the space of rapidly decreasing sequences. D. Vogt characterizes in [Math. Z. 155, 109-117 (1977; Zbl 0337.46015)] the subspaces of s in the topological category of Fréchet spaces by property (DN), proving a splitting theorem for exact sequences of Fréchet spaces and using the Komura imbedding theorem. In this paper we introduce a condition called (DNDZ) which characterizes the subspaces of s in the tame category. To do that, we show the equivalence of property (DNDZ) and a certain tame splitting theorem which is also of independent interest. Besides, we develop the concept of tame nuclearity and include a tame version of the Komura imbedding theorem.
Reviewer: M.Poppenberg

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A45 Sequence spaces (including Köthe sequence spaces)
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
Zbl 0337.46015
Full Text: DOI
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