Abstract
Let E E and F F be Banach lattices. It is shown that if F F has the Levi and the Fatou property, then the ordered Banach space L l ( E , F ) {\mathcal {L}^l}\left ( {E,F} \right ) of cone absolutely summing operators is a Banach lattice and an order ideal of the Riesz space L r ( E , F ) {\mathcal {L}^r}\left ( {E,F} \right ) of regular operators. The same argument yields a Jordan decomposition of F F -valued vector measures of bounded variation.
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