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

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0315506-7
PII: S 0002-9939(1973)0315506-7
Keywords: Weakly compact operator, positive operator, vector lattice
Article copyright: © Copyright 1973 American Mathematical Society