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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: Boris Lavrič
Journal: Proc. Amer. Math. Soc. 108 (1990), 479-481
MSC: Primary 47B10; Secondary 28B05, 47B55, 47D15
DOI: https://doi.org/10.1090/S0002-9939-1990-0993756-4
MathSciNet review: 993756
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-0993756-4
Keywords: Banach lattice, cone absolutely summing operator, vector measure
Article copyright: © Copyright 1990 American Mathematical Society