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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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A remark on Dunford-Pettis property in $L_ 1(\mu ,X)$
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by Raffaella Cilia PDF
Proc. Amer. Math. Soc. 120 (1994), 183-184 Request permission

Abstract:

We prove that if $X$ is an ${L_\infty }$ space, then ${L_1}(\mu ,X)$ has the Dunford-Pettis Property.
References
  • Kevin T. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), no.Β 1, 35–41. MR 531148, DOI 10.1007/BF01406706
  • Jean Bourgain, New classes of ${\cal L}^{p}$-spaces, Lecture Notes in Mathematics, vol. 889, Springer-Verlag, Berlin-New York, 1981. MR 639014
  • J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
    • J. Diestel, Notes on the resume of Grothendieck, preprint, 1988.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 183-184
  • MSC: Primary 46E40; Secondary 46B20, 46M05
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1176480-0
  • MathSciNet review: 1176480