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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive $p$-summing operators on $L_ p$-spaces
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by Oscar Blasco PDF
Proc. Amer. Math. Soc. 100 (1987), 275-280 Request permission

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-NikodṔm 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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 100 (1987), 275-280
  • MSC: Primary 47B10; Secondary 46B20, 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0884466-2
  • MathSciNet review: 884466