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Barrelled spaces with Boolean rings of projections.

Lech Drewnowski (1997)

Collectanea Mathematica

The talk presented a survey of results most of which have been obtained over the last several years in collaboration with M.Florencio and P.J.Paúl (Seville). The results concern the question of barrelledness of locally convex spaces equipped with suitable Boolean algebras or rings of projections. They are particularly applicable to various spaces of measurable vector valued functions. Some of the results are provided with proofs that are much simpler than the original ones.

Barrelledness of generalized sums of normed spaces

Ariel Fernández, Miguel Florencio, J. Oliveros (2000)

Czechoslovak Mathematical Journal

Let ( E i ) i ∈ I be a family of normed spaces and λ a space of scalar generalized sequences. The λ -sum of the family ( E i ) i ∈ I of spaces is λ { ( E i ) i ∈ I } : = { ( x i ) i ∈ I , x i ∈ E i , and ( ∥ x i ∥ ) i ∈ I ∈ λ } . Starting from the topology on λ and the norm topology on each E i , a natural topology on λ { ( E i ) i ∈ I } can be defined. We give conditions for λ { ( E i ) i ∈ I } to be quasi-barrelled, barrelled or locally complete.

Bases de Schauder dans certains espaces de fonctions holomorphes

Nguyen Thanh Van (1972)

Annales de l'institut Fourier

On étudie les bases de Schauder pour fonctions holomorphes et leurs applications à l’approximation et interpolation.Après avoir établi quelques faits généraux sur les bases et semi-bases, on les applique à l’étude des bases formées par une suite simple de polynômes.L’effort principal est porté sur la preuve de l’existence d’une “bonne” base commune des espaces des fonctions holomorphes sur Ω et χ , où Ω est un domaine de C et χ un compact dans Ω tels que Ω ∖ χ soit un domaine régulier pour le problème...

Bases in spaces of analytic germs

Michael Langenbruch (2012)

Annales Polonici Mathematici

We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near ℝ. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces S ¹ α and S ₁ α for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.

Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Berezin and Berezin-Toeplitz quantizations for general function spaces.

Miroslav Englis (2006)

Revista Matemática Complutense

The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic...

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