Geodesic
To the theory of operators that are bounded on cones in weighted spaces of numerical sequences
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 154-178

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the general problem of obtaining interpolation theorems for operators bounded on cones in normed spaces, and to some specific results pertaining to the particular problem of interpolation of operators bounded on cones in weighted spaces of numerical sequences. This setting is a natural generalization of the classical problem of interpolation of the boundness property of a linear operator that is bounded between two Banach couples. We introduce the general concept of a Banach triple of cones possessing the interpolation property with respect to a given Banach triple. We provide a sufficient conditions for a triple of cones $(Q_0,Q_1,Q)$ in weighted spaces of numerical sequences to possess the interpolation property with respect to a given Banach triple of weighted spaces of numerical sequences $(F_0,F_1,F)$. Appropriate interpolation theorems generalize the classical result about interpolation of linear operators in weighted spaces and are of interest for the theory of bases in Fréchet spaces. 
@article{ZNSL_2014_424_a4,
     author = {V. M. Kaplitskii and A. K. Dronov},
     title = {To the theory of operators that are bounded on cones in weighted spaces of numerical sequences},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--178},
     publisher = {mathdoc},
     volume = {424},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a4/}
}
TY  - JOUR
AU  - V. M. Kaplitskii
AU  - A. K. Dronov
TI  - To the theory of operators that are bounded on cones in weighted spaces of numerical sequences
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 154
EP  - 178
VL  - 424
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a4/
LA  - ru
ID  - ZNSL_2014_424_a4
ER  - 
%0 Journal Article
%A V. M. Kaplitskii
%A A. K. Dronov
%T To the theory of operators that are bounded on cones in weighted spaces of numerical sequences
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 154-178
%V 424
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a4/
%G ru
%F ZNSL_2014_424_a4
V. M. Kaplitskii; A. K. Dronov. To the theory of operators that are bounded on cones in weighted spaces of numerical sequences. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 154-178. http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a4/