Displaying similar documents to “Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis”

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.

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?. ...

On non-primary Fréchet Schwartz spaces

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...

Solution to a question of Grothendieck.

Jesús M. Fernández Castillo, Joaquín Motos (1992)

Extracta Mathematicae

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This note is to bring attention to one of the ending questions in Grothendieck's thesis [3, Chapter 2, p. 134]: Is the space DLp isomorphic to s ⊗ Lp? The problem has been, as we shall see, essentially solved by Valdivia and Vogt. This fact, however, seems to have remained unnoticed. Supports this belief of the authors the fact that they have been unable to find an explicit reference to its solution. ...

The space of real-analytic functions has no basis

Paweł Domański, Dietmar Vogt (2000)

Studia Mathematica

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Let Ω be an open connected subset of ℝ d . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

On exact sequences of quojections.

G. Metafune, V. B. Moscatelli (1991)

Revista Matemática de la Universidad Complutense de Madrid

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We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.

The density condition in quotients of quasinormable Fréchet spaces

Angela Albanese (1997)

Studia Mathematica

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It is proved that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Dí az in the class of separable Fréchet spaces.