We investigate a scale of -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with --estimates, and arrives at --estimates, or more generally, at estimates between K-functionals from interpolation theory.
What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of time. A twisted...
On étudie les bases de Schauder pour fonctions holomorphes et leurs applications à l’approximation et interpolation.Après avoir établi quelques faits généraux sur les bases et semi-bases, on les applique à l’étude des bases formées par une suite simple de polynômes.L’effort principal est porté sur la preuve de l’existence d’une “bonne” base commune des espaces des fonctions holomorphes sur et , où est un domaine de et un compact dans tels que soit un domaine régulier pour le problème...
We study whether the operator space can be identified with a subspace of the bidual space , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.
We investigate the behaviour of bilinear operators under limiting real methods. As an application, we show an interpolation formula for spaces of linear operators. Some results on norm estimates for bounded linear operators are also established.