Construction of standard exact sequences of power series spaces

Markus Poppenberg; Dietmar Vogt

Studia Mathematica (1995)

  • Volume: 112, Issue: 3, page 229-241
  • ISSN: 0039-3223

Abstract

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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. 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 ≤ 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. s u p n α 2 n / α n < ∞ .

How to cite

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Poppenberg, Markus, and Vogt, Dietmar. "Construction of standard exact sequences of power series spaces." Studia Mathematica 112.3 (1995): 229-241. <http://eudml.org/doc/216150>.

@article{Poppenberg1995,
author = {Poppenberg, Markus, Vogt, Dietmar},
journal = {Studia Mathematica},
keywords = {power series space of infinite or of finite type; tamely exact sequence; strongly stable; topologically exact sequence},
language = {eng},
number = {3},
pages = {229-241},
title = {Construction of standard exact sequences of power series spaces},
url = {http://eudml.org/doc/216150},
volume = {112},
year = {1995},
}

TY - JOUR
AU - Poppenberg, Markus
AU - Vogt, Dietmar
TI - Construction of standard exact sequences of power series spaces
JO - Studia Mathematica
PY - 1995
VL - 112
IS - 3
SP - 229
EP - 241
LA - eng
KW - power series space of infinite or of finite type; tamely exact sequence; strongly stable; topologically exact sequence
UR - http://eudml.org/doc/216150
ER -

References

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