Temat: Fréchet spaces - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity
Autorzy:: Domański, P.
Drewnowski, L.
Powiązania:: https://bibliotekanauki.pl/articles/1293180.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Fréchet spaces of (weakly, weak*) continuous vector-valued functions injective Fréchet spaces
spaces complemented in dual Fréchet spaces
complemented copies of $c_0$
Josefson-Nissenzweig theorem
Opis:: Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
Źródło:: Studia Mathematica; 1992, 102, 3; 257-267
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On non-primary Fréchet Schwartz spaces
Autorzy:: C. Díaz, J.
Powiązania:: https://bibliotekanauki.pl/articles/1218870.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Fréchet spaces
primary spaces
Schwartz spaces
unconditional decompositions
spaces of Moscatelli type
holomorphic functions of bounded type
Opis:: Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions of bounded type $ℋ_b(U)$, where U is a Banach space or a bounded absolutely convex open set in a Banach space.
Źródło:: Studia Mathematica; 1997, 126, 3; 291-307
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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: 4.

Tytuł:: Topological tensor products of a Fréchet-Schwartz space and a Banach space
Autorzy:: Peris, Alfredo
Powiązania:: https://bibliotekanauki.pl/articles/1292616.pdf
Data publikacji:: 1993
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Fréchet-Schwartz spaces
(DFS)-spaces
topological tensor products
approximation property
compact approximation property
Opis:: We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that $E ⊗_{ε} X$ is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for $F ⨶_π X$. This solves in the negative a question of Taskinen. We also give examples of Fréchet-Schwartz spaces and (DFS)-spaces without the compact approximation property and with the compact approximation property but without the approximation property.
Źródło:: Studia Mathematica; 1993, 106, 2; 189-196
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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