Displaying similar documents to “On inductive quadruples”

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...

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)

RACSAM

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Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.

Inductive duals of distinguished frechet spaces

José Bonet, Susanne Dierolf (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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The purpose of this note is to give an example of a distinguished Fréchet space and a non-distinguished Fréchet space which have the same inductive dual. Accordingly, distinguishedness is a property which is not reflected in the inductive dual. In contrast to this example, it was known that the properties of being quasinormable or having the density condition can be characterized in terms of the inductive dual of a Fréchet space.

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

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Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given. ...

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

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We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?. ...

Inductive limits of vector-valued sequence spaces.

José Bonet, Susanne Dierolf, Carmen Fernández (1989)

Publicacions Matemàtiques

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Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).

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...