Schwartz spaces and compact holomorphic mappings.
Schwartz spaces consistent with a duality
Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
Sequence space representations for (FN)-algebras of entire functions modulo closed ideals
Small ball properties for Fréchet spaces.
We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.
Sobre espacios (LF) metrizables.
Sobre espacios localmente convexos de Rosenthal.
Sobre los espacios Frechet-Schwartz de dimensión diametral máxima.
Sobre sumabilidad Cesáro en el espacio CS (II).
Some aspects of nuclear vector groups
In [2] W. Banaszczyk introduced nuclear groups, a Hausdorff variety of abelian topological groups which is generated by all nuclear vector groups (cf. 2.3) and which contains all nuclear vector spaces and all locally compact abelian groups. We prove in 5.6 that the Hausdorff variety generated by all nuclear vector spaces and all locally compact abelian groups (denoted by 𝒱₁) is strictly smaller than the Hausdorff variety of all nuclear groups (denoted by 𝒱₂). More precisely,...
Some aspects of the modern theory of Fréchet spaces.
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 aspects of λ(P0,N)-nuclearity.
Some locally convex spaces of regular distributions
Some properties of the tensor product of Schwartz εb-spaces.
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their εc-product Gεc(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
Spectral trajectories,duality and inductive-projective limits of Hilbert spaces
Standard exact projective resolutions relative to a countable class of Fréchet spaces
We will show that for each sequence of quasinormable Fréchet spaces there is a Köthe space λ such that and there are exact sequences of the form . If, for a fixed ℕ, is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form . The result has some applications in the theory of the functor in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
Strict inductive and projective limits, twisted spaces and quojections
Strictly Cosingular Operators on (DF)-Spaces.
Structure of spaces of holomorphic functions on infinite dimensional polydiscs
Subspaces of smooth sequence spaces