On a type of linear differential equations in Fréchet spaces

George N. Galanis

Displaying similar documents to “On a type of linear differential equations in Fréchet spaces”

On extending and lifting continuous linear mappings in topological vector spaces

W. Gejler (1978)

Studia Mathematica

Similarity:

Fréchet spaces of Moscatelli type.

José Bonet, Susanne Dierolf (1989)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

Quasinormable X-Kothe Echelon spaces.

FERNANDO BLASCO (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Similarity:

Tensor stable Fréchet and (DF)-spaces.

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

Collectanea Mathematica

Similarity:

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.

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

P. Domański, J. Krone, D. Vogt (1997)

Studia Mathematica

Similarity:

We will show that for each sequence of quasinormable Fréchet spaces ${(E_{n})}_{ℕ}$ there is a Köthe space λ such that $E x t^{1} (λ (A), λ (A) = E x t^{1} (λ (A), E_{n}) = 0$ and there are exact sequences of the form $. . . \to λ (A) \to λ (A) \to λ (A) \to λ (A) \to E_{n} \to 0$ . If, for a fixed ℕ, $E_{n}$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 \to λ (A) \to λ (A) \to E_{n} \to 0$ . The result has some applications in the theory of the functor $E x t^{1}$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.

Extension and splitting theorems for Fréchet spaces of type 2.

A. Defant, P. Domanski, M. Mastylo (1999)

Revista Matemática Complutense

Similarity:

We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).

Some results on the duals of the inductive and projective limits of Moscatelli type.

Yolanda Meléndez (1992)

Extracta Mathematicae

Similarity:

A Floquet-Liapunov theorem in Fréchet spaces

George N. Galanis, Efstathios E. Vassiliou (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

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?. ...