Construction of standard exact sequences of power series spaces

Poppenberg, Markus; Vogt, Dietmar

Studia Mathematica, Tome 113 (1995), p. 229-241 / Harvested from The Polish Digital Mathematics Library

Résumé

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 (⁎) $0 \to Λ_{R}^{p} (α) \to Λ_{R}^{p} (α) \to Λ_{R}^{p} {(α)}^{ℕ} \to 0$ exists iff α is strongly stable, i.e. $l i m_{n} α_{2 n} / α_{n} = 1$ , and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that $l i m s u p_{n} α_{K n} / α_{n} \leq A < \infty$ 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. $s u p_{n} α_{2 n} / α_{n} < \infty$ .

Publié le : 1995-01-01

Zbl 0822.46003

EUDML-ID : urn:eudml:doc:216150

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     author = {Markus Poppenberg and Dietmar Vogt},
     title = {Construction of standard exact sequences of power series spaces},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {229-241},
     zbl = {0822.46003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p229bwm}
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Poppenberg, Markus; Vogt, Dietmar. Construction of standard exact sequences of power series spaces. Studia Mathematica, Tome 113 (1995) pp. 229-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p229bwm/

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