Interpolation methods of means and orbits

Mieczys/law Masty/lo¹

¹ Faculty of Mathematics and Computer Science Adam Mickiewicz University and Institute of Mathematics Polish Academy of Sciences (Poznań branch) Umultowska 87 61-614 Poznań, Poland

Studia Mathematica, Tome 171 (2005) no. 2, pp. 153-175

Résumé

Banach operator ideal properties of the inclusion maps between Banach sequence spaces are used to study interpolation of orbit spaces. Relationships between those spaces and the method-of-means spaces generated by couples of weighted Banach sequence spaces with the weights determined by concave functions and their Janson sequences are shown. As an application we obtain the description of interpolation orbits in couples of weighted $L_p$-spaces when they are not described by the $K$-method. We also develop a connection between the method of means with a quasi-parameter and the real method of interpolation generated by the Calderón–Lozanovsky space parameters. Applications to interpolation of operators are also discussed.

Détail

DOI : 10.4064/sm171-2-3

Keywords: banach operator ideal properties inclusion maps between banach sequence spaces study interpolation orbit spaces relationships between those spaces method of means spaces generated couples weighted banach sequence spaces weights determined concave functions their janson sequences shown application obtain description interpolation orbits couples weighted p spaces described k method develop connection between method means quasi parameter real method interpolation generated calder lozanovsky space parameters applications interpolation operators discussed