Interpolation methods of means and orbits
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.