Fréchet spaces of Moscatelli type.
José Bonet, Susanne Dierolf (1989)
Revista Matemática de la Universidad Complutense de Madrid
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José Bonet, Susanne Dierolf (1989)
Revista Matemática de la Universidad Complutense de Madrid
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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.
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?. ...
P. Domański, L. Drewnowski (1992)
Studia Mathematica
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Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
Klaus-Dieter. Bierstedt, José Bonet (1989)
Revista Matemática de la Universidad Complutense de Madrid
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We survey our main results on the density condition for Fréchet spaces and on the dual density condition for (DF)-spaces (cf. Bierstedt and Bonet (1988)) as well as some recent developments.
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. ...
FERNANDO BLASCO (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Steven F. Bellenot (1980)
Compositio Mathematica
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José M. Ansemi, Socorro Ponte (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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J. Díaz (1997)
Studia Mathematica
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Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic...