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The concept of boundedness and the Bohr compactification of a MAP Abelian group

Jorge Galindo, Salvador Hernández (1999)

Fundamenta Mathematicae

Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an ℒ ∞ -group, contains “many” discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This...

The continuity of superposition operators on some sequence spaces defined by moduli

Enno Kolk, Annemai Raidjõe (2007)

Czechoslovak Mathematical Journal

Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = ( ϕ k ) let λ ( Φ ) = { x = ( x k ) ( ϕ k ( | x k | ) ) ∈ λ } . Given another sequence of modulus functions Ψ = ( ψ k ) , we characterize the continuity of the superposition operators P f from λ ( Φ ) into μ ( Ψ ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕ k ( k ∈ ...

The density condition and the strong dual density condition by operator.

Wolf-Dieter Heinrichs (1997)

Collectanea Mathematica

The aim of the present article is to introduce and investigate topological properties by operator. We obtain good stability properties for the density condition and the strong dual density condition by taking injective tensor products. Further we analyze the connection to (DF)-properties by operator.

The density condition in projective tensor products.

Wolf-Dieter Heinrichs (1999)

Revista Matemática Complutense

In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.

The density condition in quotients of quasinormable Fréchet spaces

Angela Albanese (1997)

Studia Mathematica

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.

The Dirichlet problem for Baire-one functions

Jiří Spurný (2004)

Open Mathematics

Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.

The distance between subdifferentials in the terms of functions

Libor Veselý (1993)

Commentationes Mathematicae Universitatis Carolinae

For convex continuous functions f , g defined respectively in neighborhoods of points x , y in a normed linear space, a formula for the distance between ∂ f ( x ) and ∂ g ( y ) in terms of f , g (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...

The dual of the space of holomorphic functions on locally closed convex sets.

José Bonet, Reinhold Meise, Sergej N. Melikhov (2005)

Publicacions Matemàtiques

Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.

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