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Proceedings of the American Mathematical Society

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

 

 

The regularity of Dunford-Pettis operators


Author: James R. Holub
Journal: Proc. Amer. Math. Soc. 104 (1988), 89-95
MSC: Primary 47B37; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0958049-0
MathSciNet review: 958049
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Abstract: Let $ \lambda $ denote a symmetric, solid Banach sequence space having $ \left\{ {{e_i}} \right\}_{i = 1}^\infty $ as a symmetric basis and considered as a Banach lattice with order defined coordinatewise. A complete description of the relationship between regular and Dunford-Pettis operators $ T:{L^1}[0,1] \to \lambda $ is given. The results obtained complete earlier work of Gretsky and Ostroy and of the author in this area.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0958049-0
Keywords: Dunford-Pettis operator, regular operator
Article copyright: © Copyright 1988 American Mathematical Society