Temat: nuclear spaces - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Standard exact projective resolutions relative to a countable class of Fréchet spaces
Autorzy:: Domański, P.
Krone, J.
Vogt, D.
Powiązania:: https://bibliotekanauki.pl/articles/1220055.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Fréchet spaces
Köthe sequence spaces
splitting of short exact sequences
nuclear spaces
Schwartz spaces
quasinormable spaces
functor $Ext^1$
projective spaces
projective resolution
Opis:: 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.
Źródło:: Studia Mathematica; 1997, 123, 3; 275-290
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A splitting theory for the space of distributions
Autorzy:: Domański, P.
Vogt, D
Powiązania:: https://bibliotekanauki.pl/articles/1206085.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: exact complex
systems of partial differential equations
short exact sequence
splitting
space of distributions
lifting of Banach discs
Schwartz spaces
nuclear spaces
ultrabornological associated space
ω
Opis:: 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'
Źródło:: Studia Mathematica; 2000, 140, 1; 57-77
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Series representation of compact linear operators in Banach spaces
Autorzy:: Edmunds, David E.
Lang, Jan
Powiązania:: https://bibliotekanauki.pl/articles/745232.pdf
Data publikacji:: 2016
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Eigenvalues
Banach spaces
compact operators
nuclear maps
Gelfand numbers
Opis:: Let $p\in(1,\infty)$ and $I=(0,1)$; suppose that $T\colon L_{p}(I)\rightarrow L_{p}(I)$ is a~compact linear map with trivial kernel and range dense in $L_{p}(I)$. It is shown that if the Gelfand numbers of $T$ decay sufficiently quickly, then the action of $T$ is given by a series with calculable coefficients. The special properties of $L_{p}(I)$ enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
Źródło:: Commentationes Mathematicae; 2016, 56, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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