Interpolation methods of means and orbits

Mieczysław Mastyło. "Interpolation methods of means and orbits." Studia Mathematica 171.2 (2005): 153-175. <http://eudml.org/doc/284953>.

@article{MieczysławMastyło2005,
abstract = {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.},
author = {Mieczysław Mastyło},
journal = {Studia Mathematica},
keywords = {interpolation orbit; method of means; Calderón-Lozanovsky method; weighted Banach lattice; Calderón couple; -method; ; 1)},
language = {eng},
number = {2},
pages = {153-175},
title = {Interpolation methods of means and orbits},
url = {http://eudml.org/doc/284953},
volume = {171},
year = {2005},
}

TY - JOUR
AU - Mieczysław Mastyło
TI - Interpolation methods of means and orbits
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 2
SP - 153
EP - 175
AB - 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.
LA - eng
KW - interpolation orbit; method of means; Calderón-Lozanovsky method; weighted Banach lattice; Calderón couple; -method; ; 1)
UR - http://eudml.org/doc/284953
ER -