Some properties of the Pisier-Zu interpolation spaces

Volume 65 / 1993

A. Sersouri Colloquium Mathematicum 65 (1993), 43-50 DOI: 10.4064/cm-65-1-43-50


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 $A_{*}(η)$ [the isometric predual of A(η)]. All the results of this paper extend, with obvious changes in the proofs, to the interpolation spaces $[v_1(I),C(I)]_{θq}$.


  • A. Sersouri

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