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

Domański, P.; Krone, J.; Vogt, D.

Domański, P. ; Krone, J. ; Vogt, D.

Studia Mathematica, Tome 122 (1997), p. 275-290 / Harvested from The Polish Digital Mathematics Library

Résumé

We will show that for each sequence of quasinormable Fréchet spaces ${(E_{n})}_{ℕ}$ there is a Köthe space λ such that $E x t^{1} (λ (A), λ (A) = E x t^{1} (λ (A), E_{n}) = 0$ and there are exact sequences of the form $. . . \to λ (A) \to λ (A) \to λ (A) \to λ (A) \to E_{n} \to 0$ . 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 $0 \to λ (A) \to λ (A) \to E_{n} \to 0$ . The result has some applications in the theory of the functor $E x t^{1}$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.

Publié le : 1997-01-01

Zbl 0910.46001

EUDML-ID : urn:eudml:doc:216393

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     author = {P. Doma\'nski and J. Krone and D. Vogt},
     title = {Standard exact projective resolutions relative to a countable class of Fr\'echet spaces},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {275-290},
     zbl = {0910.46001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p275bwm}
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Domański, P.; Krone, J.; Vogt, D. Standard exact projective resolutions relative to a countable class of Fréchet spaces. Studia Mathematica, Tome 122 (1997) pp. 275-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p275bwm/

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