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Construction of standard exact sequences of power series spaces

Markus PoppenbergDietmar Vogt — 1995

Studia Mathematica

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 ) 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 < .

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