Construction of standard exact sequences of power series spaces
Studia Mathematica, Tome 112 (1994) no. 3, pp. 229-241
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The following result is proved: Let $Λ_R^p(α)$ denote a power series space of infinite or of finite type, and equip $Λ_R^p(α)$ with its canonical fundamental system of norms, R ∈ {0,∞}, 1 ≤ p ∞. Then a tamely exact sequence (⁎) $0 → Λ_{R}^{p}(α) → Λ_{R}^{p}(α) → Λ_{R}^{p}(α)^ℕ → 0$ exists iff α is strongly stable, i.e. $lim_n α_{2n}/α_n = 1$, and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that $lim sup_n α_{Kn}/α_n ≤ A ∞$ for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable, i.e. $sup_n α_{2n}/α_n ∞$.
@article{10_4064_sm_112_3_229_241,
author = {Markus Poppenberg and },
title = {Construction of standard exact sequences of power series spaces},
journal = {Studia Mathematica},
pages = {229--241},
publisher = {mathdoc},
volume = {112},
number = {3},
year = {1994},
doi = {10.4064/sm-112-3-229-241},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-112-3-229-241/}
}
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%0 Journal Article %A Markus Poppenberg %A %T Construction of standard exact sequences of power series spaces %J Studia Mathematica %D 1994 %P 229-241 %V 112 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-112-3-229-241/ %R 10.4064/sm-112-3-229-241 %G en %F 10_4064_sm_112_3_229_241
Markus Poppenberg; . Construction of standard exact sequences of power series spaces. Studia Mathematica, Tome 112 (1994) no. 3, pp. 229-241. doi: 10.4064/sm-112-3-229-241
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