Weakly compact positive operators on summable functions
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- by Paul C. Shields PDF
- Proc. Amer. Math. Soc. 37 (1973), 456-458 Request permission
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
- Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 2020, DOI 10.1090/S0002-9947-1940-0002020-4
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Hidegorô Nakano, Product spaces of semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 12 (1953), 163–210. MR 0062961
Additional Information
- © Copyright 1973 American Mathematical Society
- 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