Every separable Fréchet space contains a non stable dense subspace

Ed Dubinsky

Displaying similar documents to “Every separable Fréchet space contains a non stable dense subspace”

Geometrical properties of Banach spaces and the distribution of the norm for a stable measure

Michał Ryznar (1988)

Studia Mathematica

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On the three-space property: non-containment of l, 1 ≤ p < ∞, or c subspaces.

Juan Carlos Díaz Alcaide (1993)

Publicacions Matemàtiques

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The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to l, 1 ≤ p < ∞, or to c. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.

On the convergence of superpositions of a sequence of operators

M. Reichaw (1965)

Studia Mathematica

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Construction of standard exact sequences of power series spaces

Markus Poppenberg, Dietmar Vogt (1995)

Studia Mathematica

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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 (⁎) $0 \to Λ_{R}^{p} (α) \to Λ_{R}^{p} (α) \to Λ_{R}^{p} {(α)}^{ℕ} \to 0$ 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 $l i m s u p_{n} α_{K n} / α_{n} \leq A < \infty$ for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable,...

The uncomplemented subspace K(E,F)

Alfred Tong, Donald Wilken (1971)

Studia Mathematica

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The space $D (U)$ is not $B_{r}$ -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

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Certain classes of locally convex space having non complete separated quotients are studied and consequently results about $B_{r}$ -completeness are obtained. In particular the space of L. Schwartz $D (Ω)$ is not $B_{r}$ -complete where $Ω$ denotes a non-empty open set of the euclidean space $R^{m}$ .

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Quotients and interpolation spaces of stable Banach spaces

J. Bastero, Y. Raynaud (1989)

Studia Mathematica

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Strongly nonnorming subspaces and prequojections

Vincenzo Moscatelli (1990)

Studia Mathematica

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Structure theory of power series spaces of infinite type.

Dietmar Vogt (2003)

RACSAM

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The paper gives a complete characterization of the subspaces, quotients and complemented subspaces of a stable power series space of infinite type without the assumption of nuclearity, so extending previous work of M. J. Wagner and the author to the nonnuclear case. Various sufficient conditions for the existence of bases in complemented subspaces of infinite type power series spaces are also extended to the nonnuclear case.