Tame spaces and power series spaces
For tame Fréchet spaces in the sense of \textit{R. S. Hamilton}, [Bull. Am. Math. Soc. 7, 65-222 (1982; Zbl 0499.58003)] or \textit{F. Sergeraert} [Ann. Sci. Éc. Norm. Sup., IV Sér. 5, 599-660 (1972; Zbl 0246.58006)] we prove the following theorems: I. Theorem: If \(0\to F\to G\to ^{q}H\to 0\) is a tame exact sequence of tame Fréchet spaces, one of which is nuclear, then it splits tamely, i.e. q has a tame right inverse. II. Theorem: Every nuclear tame Fréchet space is tamely equivalent to a power series space of infinite type.
every nuclear tame Fréchet space is tamely equivalent to a power series space of infinite type
scientific article; zbMATH DE number 4009066
scientific article