Displaying similar documents to “Strong duals of projective limits of (LB)-spaces”

Acyclic inductive spectra of Fréchet spaces

Jochen Wengenroth (1996)

Studia Mathematica

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We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem...

The projective limit functor for spectra of webbed spaces

L. Frerick, D. Kunkle, J. Wengenroth (2003)

Studia Mathematica

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We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.

Biduality in (LF)-spaces.

Klaus D. Bierstedt, José Bonet (2001)

RACSAM

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En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = ind E un espacio (LF), ponemos H = ind H para una sucesión de subespacios de Fréchet H de E con H ⊂ H. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H')' o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...

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

P. Domański, J. Krone, D. Vogt (1997)

Studia Mathematica

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We will show that for each sequence of quasinormable Fréchet spaces ( E n ) ℕ there is a Köthe space λ such that E x t 1 ( λ ( A ) , λ ( A ) = E x t 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 E x t 1 in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.