Some properties of the Pisier-Zu interpolation spaces

A. Sersouri

ArticleOriginal scientific text

Title

Some properties of the Pisier-Zu interpolation spaces

Authors ¹

Affiliations

C.N.R., B.P. 1346 R.P., Rabat, Morocco

Abstract

For a closed subset I of the interval [0,1] we let A(I) = [v_1(I),C(I)]_{(1/2)2}. We show that A(I) is isometric to a 1-complemented subspace of A(0,1), and that the Szlenk index of A(I) is larger than the Cantor index of I. We also investigate, for ordinals η < ω_1, the bases structures of A(η), A*(η), and

A_{\cdot} (η)

[the isometric predual of A(η)]. All the results of this paper extend, with obvious changes in the proofs, to the interpolation spaces

{[v_{1} (I), C (I)]}_{θ q}

.

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Title

Some properties of the Pisier-Zu interpolation spaces

Affiliations

Abstract

Bibliography