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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Steven F. Bellenot (1980)
Compositio Mathematica
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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.
Paweł Domański, Dietmar Vogt (2000)
Studia Mathematica
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Let Ω be an open connected subset of . 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.
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...
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.
José Bonet, Susanne Dierolf (1989)
Revista Matemática de la Universidad Complutense de Madrid
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Andreas Benndorf (1983)
Studia Mathematica
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Dietmar Vogt (1987)
Studia Mathematica
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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?. ...
FERNANDO BLASCO (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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