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

 

The hereditary Dunford-Pettis property for $ l\sb 1(E)$


Author: Pilar Cembranos
Journal: Proc. Amer. Math. Soc. 108 (1990), 947-950
MSC: Primary 46B15; Secondary 46E40
MathSciNet review: 1004415
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Abstract: A Banach space $ E$ is said to be hereditarily Dunford-Pettis if all of its closed subspaces have the Dunford-Pettis property. In this note we prove that the Banach space $ {l_1}(E)$, of all absolutely summing sequences in $ E$ with the usual norm, is hereditarily Dunford-Pettis if and only if $ E$ is also.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1004415-6
PII: S 0002-9939(1990)1004415-6
Article copyright: © Copyright 1990 American Mathematical Society