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1

A splitting theory for the space of distributions

100%

Domański P., Vogt D.

Studia Mathematica

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2000

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tom 140

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nr 1

57-77

EN

The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'

2

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

81%

Domański P., Krone J., Vogt D.

Studia Mathematica

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1997

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tom 123

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nr 3

275-290

EN

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

3

Fréchet quotients of spaces of real-analytic functions

81%

Domański P., Frerick L., Vogt D.

Studia Mathematica

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2003

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tom 159

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nr 2

229-245

EN

We characterize all Fréchet quotients of the space 𝒜(Ω) of (complex-valued) real-analytic functions on an arbitrary open set $Ω ⊆ ℝ^{d}$. We also characterize those Fréchet spaces E such that every short exact sequence of the form 0 → E → X → 𝒜(Ω) → 0 splits.

Ograniczanie wyników

3 Studia Mathematica

3 Domański P.

3 Vogt D.

1 Frerick L.

1 Krone J.

1 2003

1 2000

1 1997

A splitting theory for the space of distributions

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

Fréchet quotients of spaces of real-analytic functions