On the modulus of cone absolutely summing operators and vector measures of bounded variation

Lavrič, Boris

doi:10.1090/S0002-9939-1990-0993756-4

On the modulus of cone absolutely summing operators and vector measures of bounded variation
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by Boris Lavrič PDF

Proc. Amer. Math. Soc. 108 (1990), 479-481 Request permission

Abstract:

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

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