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Étude des projections de norme 1 de $E^{''}$ sur $E$ . Unicité de certains préduaux. Applications

Gilles Godefroy (1979)

Annales de l'institut Fourier

On étudie dans ce travail les projections de norme 1 du bidual $E^{''}$ d’un espace de Banach $E$ sur l’image canonique $i_{E} (E)$ de $E$ dans $E^{''}$ . On montre que dans un certain nombre de cas, il y a unicité de la projection de norme 1. On en déduit des théorèmes d’existence et d’unicité du prédual de $E$ . On donne ensuite diverses applications, en particulier aux espaces dont la norme est différentiable sur un ensemble dense et aux espaces ne contenant pas $ℓ^{1} (N)$ .

Examples of k-iterated spreading models

Spiros A. Argyros, Pavlos Motakis (2013)

Studia Mathematica

It is shown that for every k ∈ ℕ and every spreading sequence eₙₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space $X_{k + 1}$ admitting eₙₙ as a k+1-iterated spreading model, but not as a k-iterated one.

Exemples d'espaces de Banach ayant la propriété de projection uniforme

C. Samuel (1977/1978)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Exemples d'espaces de Banach ayant la propriété de projection uniforme

C. Samuel (1980)

Colloquium Mathematicae

Extension of linear operators and Lipschitz maps into $𝒞 (K)$ -spaces.

Kalton, N.J. (2007)

The New York Journal of Mathematics [electronic only]

Extension of multilinear operators on Banach spaces.

Félix Cabello Sánchez, R. García, I. Villanueva (2000)

Extracta Mathematicae

These notes deal with the extension of multilinear operators on Banach spaces. The organization of the paper is as follows. In the first section we study the extension of the product on a Banach algebra to the bidual and some related structures including modules and derivations. Tha approach is elementary and uses the classical Arens' technique. Actually most of the results of section 1 can be easily derived from section 2. In section 2 we consider the problem of extending multilinear forms on a...