Geodesic
On Riesz spaces with $b$-property and $b$-weakly compact operators
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 19-26

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An operator $T\colon E\to X$ between a Banach lattice $E$ and a Banach space $X$ is called $b$-weakly compact if $T(B)$ is relatively weakly compact for each $b$-bounded set $B$ in $E$. We characterize $b$-weakly compact operators among $o$-weakly compact operators. We show summing operators are $b$-weakly compact and discuss relation between Dunford–Pettis and $b$-weakly compact operators. We give necessary conditions for $b$-weakly compact operators to be compact and give characterizations of $K\!B$-spaces in terms of $b$-weakly compact operators defined on them. 
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     author = {\c{S}. Alpay and B. Altin},
     title = {On {Riesz} spaces with $b$-property and $b$-weakly compact operators},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {19--26},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a2/}
}
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Ş. Alpay; B. Altin. On Riesz spaces with $b$-property and $b$-weakly compact operators. Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 19-26. http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a2/