Displaying similar documents to “Acyclic inductive spectra of Fréchet spaces”

Strong duals of projective limits of (LB)-spaces

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

Czechoslovak Mathematical Journal

Similarity:

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...

Biduality in (LF)-spaces.

Klaus D. Bierstedt, José Bonet (2001)

RACSAM

Similarity:

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...

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)

RACSAM

Similarity:

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.

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

Similarity:

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

Similarity:

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?. ...