Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 73-80
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B. M. Makarov. A characteristic of invariant order-hounded sets in the space $L^p(\Omega,\mu)$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 73-80. http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a4/
@article{ZNSL_1974_47_a4,
author = {B. M. Makarov},
title = {A~characteristic of invariant order-hounded sets in the space $L^p(\Omega,\mu)$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {73--80},
year = {1974},
volume = {47},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a4/}
}
TY - JOUR
AU - B. M. Makarov
TI - A characteristic of invariant order-hounded sets in the space $L^p(\Omega,\mu)$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1974
SP - 73
EP - 80
VL - 47
UR - http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a4/
LA - ru
ID - ZNSL_1974_47_a4
ER -
%0 Journal Article
%A B. M. Makarov
%T A characteristic of invariant order-hounded sets in the space $L^p(\Omega,\mu)$
%J Zapiski Nauchnykh Seminarov POMI
%D 1974
%P 73-80
%V 47
%U http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a4/
%G ru
%F ZNSL_1974_47_a4
Necessary and sufficient conditions are established for the image $U(B)$ of a set $B\subset L^p$ to be order-bounded in $L^p$ under arbitrary linear continuous mapping $U\colon L^p\to L^p$. The proof is based on properties of absolutely $p$-summing operators.
