Geodesic
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

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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. 
@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},
     publisher = {mathdoc},
     volume = {47},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a4/}
}
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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/