Interpolation methods of means and orbits

Volume 171 / 2005

Mieczys/law Masty/lo Studia Mathematica 171 (2005), 153-175 MSC: Primary 46B70. DOI: 10.4064/sm171-2-3


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.


  • Mieczys/law Masty/loFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Institute of Mathematics
    Polish Academy of Sciences (Poznań branch)
    Umultowska 87
    61-614 Poznań, Poland

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