DOMINATION BY POSITIVE WEAK DUNFORD–PETTIS OPERATORS ON BANACH LATTICES
2014 ◽
Vol 90
(2)
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pp. 311-318
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AbstractRecently, H’michane et al. [‘On the class of limited operators’, Acta Math. Sci. (submitted)] introduced the class of weak$^*$ Dunford–Pettis operators on Banach spaces, that is, operators which send weakly compact sets onto limited sets. In this paper, the domination problem for weak$^*$ Dunford–Pettis operators is considered. Let $S, T:E\to F$ be two positive operators between Banach lattices $E$ and $F$ such that $0\leq S\leq T$. We show that if $T$ is a weak$^{*}$ Dunford–Pettis operator and $F$ is $\sigma $-Dedekind complete, then $S$ itself is weak$^*$ Dunford–Pettis.
1977 ◽
Vol 29
(5)
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pp. 963-970
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2002 ◽
Vol 65
(2)
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pp. 223-230
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Keyword(s):
1972 ◽
pp. 235-274
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Keyword(s):
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1993 ◽
Vol 36
(4)
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pp. 407-413
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