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Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz (1997)

Collectanea Mathematica

A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.

Embedding c 0 in bvca ( Σ , X )

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

Equivanishing sequences of mappings

Piotr Antosik (2000)

Banach Center Publications

Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems

Essentially Incomparable Banach Spaces of Continuous Functions

Rogério Augusto dos Santos Fajardo (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We construct, under Axiom ♢, a family ( C ( K ξ ) ) ξ < 2 ( 2 ω ) of indecomposable Banach spaces with few operators such that every operator from C ( K ξ ) into C ( K η ) is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable. Assuming no additional set-theoretic axiom, we obtain this result with size 2 ω instead of 2 ( 2 ω ) .

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 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.

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...

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