Standard exact projective resolutions relative to a countable class of Fréchet spaces

Volume 123 / 1997

P. Domański, , Studia Mathematica 123 (1997), 275-290 DOI: 10.4064/sm-123-3-275-290


We will show that for each sequence of quasinormable Fréchet spaces $(E_n)_ℕ$ there is a Köthe space λ such that $Ext^1(λ(A), λ(A) = Ext^1 (λ(A), E_n)=0$ and there are exact sequences of the form $... → λ(A) → λ(A) → λ(A) → λ(A) → {E_n} → 0$. If, for a fixed ℕ, $E_n$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 → λ(A) → λ(A) → {E_n} → 0$. The result has some applications in the theory of the functor $Ext^1$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.


  • P. Domański

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