An ordinal version of some applications of the classical interpolation theorem

Benoît Bossard

ArticleOriginal scientific text

Title

An ordinal version of some applications of the classical interpolation theorem

Authors ¹

Affiliations

Equipe d'Analyse, Université Paris VI, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France

Abstract

Let E be a Banach space with a separable dual. Zippin's theorem asserts that E embeds in a Banach space

E_{1}

with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space

E_{2}

with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of

E_{1}

and

E_{2}

can be controlled by the Szlenk index of E, where the Szlenk index is an ordinal index associated with a separable Banach space which provides a transfinite measure of the separability of the dual space.

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Title

An ordinal version of some applications of the classical interpolation theorem

Affiliations

Abstract

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