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Ensembles de Rosenthal et propriété de Radon-Nikodym relative

Mohammad Daher (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

Soient G un groupe abélien compact métrisable, Γ son groupe dual et Λ ⊂ Γ un ensemble de Rosenthal. Nous montrons que L Λ ∞ ( G , Y * ) = C Λ ( G , Y * ) , lorsque Y * est un espace de Banach ayant la propriété de Radon-Nikodym et C Λ ( G , Y * ) est faiblement séquentiellement complet. Nous en déduisons une condition suffisante pour que le produit de deux ensembles de Rosenthal en soit encore un pour le groupe produit. Ensuite nous introduisons la propriété de Radon-Nikodym relative R N - Λ , une généralisation de la propriété de Radon-Nikodym analytique....

Ensembles singuliers associés aux espaces de Banach réticulés

Denis Feyel (1981)

Annales de l'institut Fourier

À tout espace de Banach fonctionnel réticulé est associée une quasi-topologie. Avec une hypothèse de dénombrabilité convenable, cette notion généralise la topologie polonaise classique. Les ensembles singuliers sont les ensembles discrets, clairsemés etc. que l’on caractérise à l’aide des mesures qu’ils portent. Le théorème de Baire admet aussi une généralisation. Application est faite au modèle probabiliste et à la théorie du potentiel.

Entropy numbers of general diagonal operators.

Thomas Kühn (2005)

Revista Matemática Complutense

We determine the asymptotic behavior of the entropy numbers of diagonal operators D: lp → lq, (xk) → (skxk), 0 < p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σk). Our results extend the known estimates for polynomial and logarithmic diagonals (σk). Moreover, we also consider some exotic intermediate examples like (σk)=exp(-√log k).

Envelope functions and asymptotic structures in Banach spaces

Bünyamin Sarı (2004)

Studia Mathematica

We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic- ℓ p spaces in terms of the ℓ p -behavior of “disjoint-permissible” vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey-Pisier theorem.

Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

Equilateral sets in Banach spaces of the form C(K)

Sophocles K. Mercourakis, Georgios Vassiliadis (2015)

Studia Mathematica

We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.

Equivalence Between K-functionals Based on Continuous Linear Transforms

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University....

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