caa a22 4500 605526060 CHVBK 20210128100801.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2524-0 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2524-0 To the Theory of Operators that are Bounded on Cones in Weighted Spaces of Numerical Sequences [Elektronische Daten] [V. Kaplitskii, A. Dronov] The paper is devoted to the general problem of obtaining interpolation theorems for operators that are bounded on cones in normed spaces and to some specific results pertaining to the particular problem of interpolation of operators that are bounded on cones in weighted spaces of numerical sequences. This setting is a natural generalization of the classical problem of interpolation of the boundedness property for 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 sufficient conditions under which a triple of cones (Q0,Q1,Q) in weighted spaces of numerical sequences possesses the interpolation property with respect to a given Banach triple of weighted spaces of numerical sequences (F0, F1, 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. Bibliography: 10 titles. Springer Science+Business Media New York, 2015 Kaplitskii V. Southern Federal University, Rostov-on-Don, Russia aut Dronov A. Southern Federal University, Rostov-on-Don, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/5(2015-09-01), 761-777 1072-3374 209:5<761 2015 209 10958 https://doi.org/10.1007/s10958-015-2524-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2524-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kaplitskii V. Southern Federal University, Rostov-on-Don, Russia aut NATIONALLICENCE 700 1- Dronov A. Southern Federal University, Rostov-on-Don, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/5(2015-09-01), 761-777 1072-3374 209:5<761 2015 209 10958