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The Hereditary Dunford-Pettis Property On C(K,E)


Cembranos, Pilar (1984) The Hereditary Dunford-Pettis Property On C(K,E). Illinois Journal of Mathematics, 91 (4). pp. 556-558. ISSN 0019-2082

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The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the hereditary Dunford-Pettis property; (b) C(K) and c0(X) have the hereditary Dunford-Pettis property. Unwilling to give up here, the author provides an elegant characterization of when c0(X) has the hereditary Dunford-Pettis property. Since the paper was written, Nunez has provided an elegant example (based on work of Talagrand) of an X such that, while X is hereditarily Dunford-Pettis, c0(X) is not. Remarkable and satisfying!

Item Type:Article
Uncontrolled Keywords:Mathematics; Applied; Mathematics
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:14953

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