The space of real-analytic functions has no basis

Paweł Domański; Dietmar Vogt

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Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis

Steven F. Bellenot (1980)

Compositio Mathematica

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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 D_L^p isomorphic to s ⊗ L^p? 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. ...

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.

Unsolved Problems

N. Aronszajn, L. Gross, S. Kwapień, N. Nielsen, A. Pełczyński, A. Pietsch, L. Schwartz, P. Saphar, S. Chevet, R. Dudley, D. Garling, N. Kalton, B. Mitjagin, S. Rolewicz, E. Schock, J. Daleckiĭ, J. Dobrakov, B. Gelbaum, G. Henkin, L. Nachbin, N. Peck, L. Waelbroeck, P. Porcelli, M. Rao, M. Zerner, V. Zakharjuta (1970)

Studia Mathematica

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1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

On the relation of the bounded approximation property and a finite dimensional decomposition in nuclear Fréchet spaces

Andreas Benndorf (1983)

Studia Mathematica

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Quasinormable X-Kothe Echelon spaces.

FERNANDO BLASCO (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Some remarks on Dragilev's theorem

C. Bessaga (1968)

Studia Mathematica

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