Geodesic
Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 442-447

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We obtain some necessary and some sufficient conditions on Banach lattices $E$ and $F$ such that (i) if $T\colon E\to F$ is a $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T'\colon F'\to E'$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator and (ii) if $T'\colon F'\to E'$ is $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T\colon E\to F$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator.
Keywords: Banach lattice, $\mathrm{b}$-$\mathrm{AM}$-compact operator, discrete space. 
@article{MZM_2013_93_3_a11,
     author = {Na Cheng and Zi-Li Chen and Guang-Gui Chen},
     title = {Duality {Properties} for $\mathrm{b}$-$\mathrm{AM}${-Compact} {Operators} on {Banach} {Lattices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {442--447},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a11/}
}
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Na Cheng; Zi-Li Chen; Guang-Gui Chen. Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 442-447. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a11/