Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 753-760
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Yu. V. Pokornyi; S. V. Smitskikh. Inversion of the oscillatory property of focusing operators. Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 753-760. http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a15/
@article{MZM_1976_20_5_a15,
author = {Yu. V. Pokornyi and S. V. Smitskikh},
title = {Inversion of the oscillatory property of focusing operators},
journal = {Matemati\v{c}eskie zametki},
pages = {753--760},
year = {1976},
volume = {20},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a15/}
}
TY - JOUR
AU - Yu. V. Pokornyi
AU - S. V. Smitskikh
TI - Inversion of the oscillatory property of focusing operators
JO - Matematičeskie zametki
PY - 1976
SP - 753
EP - 760
VL - 20
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a15/
LA - ru
ID - MZM_1976_20_5_a15
ER -
%0 Journal Article
%A Yu. V. Pokornyi
%A S. V. Smitskikh
%T Inversion of the oscillatory property of focusing operators
%J Matematičeskie zametki
%D 1976
%P 753-760
%V 20
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a15/
%G ru
%F MZM_1976_20_5_a15
Suppose that $E$ is a real Banach space with a cone $K$ and suppose that the homogeneous additive operator $A$ that is positive on $K$ is focusing, i.e., $AK\subset K_{u_0\rho}$ for certain $u_0\in K$ and $\rho\ge1$. Then, as is well known, the operator $A$ uniformly reduces the oscillation (osc) between the elements of $K$. In this paper we show that only the focusing operators have this property.
