Displaying similar documents to “Fréchet-spaces-valued measures and the AL-property.”

Complemented copies of c in vector-valued Köthe-Dieudonné function spaces.

Santiago Díaz, Antonio Fernandez, Miguel Florencio, Pedro J. Paúl (1992)

Collectanea Mathematica

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Let [Lambda] be a barrelled perfect (in the sense of J. Dieudonné) Köthe space of measurable functions defined on an atomless finite Radon measure space. Let X be a Banach space containing a copy of c0, then the space [Lambda(X)] of [Lambda]-Bochner integrable functions contains a complemented copy of c0.

Conical measures and properties of a vector measure determined by its range

L. Rodríguez-Piazza, M. Romero-Moreno (1997)

Studia Mathematica

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We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...

Tensor stable Fréchet and (DF)-spaces.

José Bonet, Juan Carlos Díaz, Jari Taskinen (1991)

Collectanea Mathematica

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In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are 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?. ...

Some normability conditions on Fréchet spaces.

Tosun Terzioglu, Dietmar Vogt (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We define two new normability conditions on Fréchet spaces and announce some related results.

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. ...