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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive $ p$-summing operators on $ L\sb p$-spaces


Author: Oscar Blasco
Journal: Proc. Amer. Math. Soc. 100 (1987), 275-280
MSC: Primary 47B10; Secondary 46B20, 47B38
MathSciNet review: 884466
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Abstract: It is shown that for any Banach space $ B$ every positive $ p$-summing operator from $ {L^{p'}}(\mu )$ in $ B$, $ 1/p + 1/p' = 1$, is also cone absolutely summing. We also prove here that a necessary and sufficient condition that $ B$ has the Radon-NikodPm property is that every positive $ p$-summing operator $ T:{L^{p'}}(\mu ) \to B$ is representable by a function $ f$ in $ {L^p}(\mu ,B)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884466-2
PII: S 0002-9939(1987)0884466-2
Keywords: $ p$-summing operator, cone absolutely summing, Radon-Nikodým property
Article copyright: © Copyright 1987 American Mathematical Society