The hereditary Dunford-Pettis property for 𝑙₁(𝐸)

Cembranos, Pilar

doi:10.1090/S0002-9939-1990-1004415-6

The hereditary Dunford-Pettis property for $l_ 1(E)$
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Proc. Amer. Math. Soc. 108 (1990), 947-950 Request permission

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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