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

P. Domański; J. Krone; D. Vogt

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Displaying similar documents to “Standard exact projective resolutions relative to a countable class of Fréchet spaces”

A splitting theory for the space of distributions

P. Domański, D. Vogt (2000)

Studia Mathematica

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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'

On the functors Ext¹(E,F) for Fréchet spaces

Dietmar Vogt (1987)

Studia Mathematica

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Fréchet valued co-echelon spaces

Elisabetta M. Mangino (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Strong duals of projective limits of (LB)-spaces

J. Bonet, Susanne Dierolf, J. Wengenroth (2002)

Czechoslovak Mathematical Journal

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We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit...

On a type of linear differential equations in Fréchet spaces

George N. Galanis (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...

Fréchet spaces of Moscatelli type.

José Bonet, Susanne Dierolf (1989)

Revista Matemática de la Universidad Complutense de Madrid

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Solution to a question of Grothendieck.

Jesús M. Fernández Castillo, Joaquín Motos (1992)

Extracta Mathematicae

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This note is to bring attention to one of the ending questions in Grothendieck's thesis [3, Chapter 2, p. 134]: Is the space D_L^p isomorphic to s ⊗ L^p? The problem has been, as we shall see, essentially solved by Valdivia and Vogt. This fact, however, seems to have remained unnoticed. Supports this belief of the authors the fact that they have been unable to find an explicit reference to its solution. ...

On exact sequences of quojections.

G. Metafune, V. B. Moscatelli (1991)

Revista Matemática de la Universidad Complutense de Madrid

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We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.