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Weakly compact positive operators on summable functions


Author: Paul C. Shields
Journal: Proc. Amer. Math. Soc. 37 (1973), 456-458
MSC: Primary 47B55; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1973-0315506-7
MathSciNet review: 0315506
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Abstract: This paper uses elementary integration and operator techniques combined with some theorems of Nakano to give a simple proof of the well-known Dunford-Pettis theorem for positive operators.


References [Enhancements On Off] (What's this?)

  • [1] N. Dunford and B. J. Pettis, Linear operations on summable functions. Trans. Amer. Math. Soc. 47 (1940), 323-392. MR 1, 338. MR 0002020 (1:338b)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] H. Nakano, Product spaces of semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I 12 (1953), 163-210. MR 16, 49. MR 0062961 (16:49f)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315506-7
Keywords: Weakly compact operator, positive operator, vector lattice
Article copyright: © Copyright 1973 American Mathematical Society

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