About: Dunford–Pettis property

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In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C(K) of continuous functions on a compact space and the space L1(μ) of the Lebesgue integrable functions on a measure space. Alexander Grothendieck introduced the concept in the early 1950s, following the work of Dunford and Pettis, who developed earlier results of Shizuo Kakutani, Kōsaku Yosida, and several others. Important results were obtained more recently by Jean Bourgain. Nevertheless, the Dunford–Pettis property is not completely understood.

Attributes	Values
rdf:type	yago:WikicatBanachSpaces yago:Abstraction100002137 yago:Attribute100024264 building yago:Space100028651
rdfs:label	Dunford–Pettis property (en) Dunford-Pettis-Eigenschaft (de)
rdfs:comment	Die Dunford-Pettis-Eigenschaft (nach N. Dunford und B. J. Pettis) ist eine im mathematischen Teilgebiet der Funktionalanalysis betrachtete Eigenschaft von Banachräumen. (de) In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C(K) of continuous functions on a compact space and the space L1(μ) of the Lebesgue integrable functions on a measure space. Alexander Grothendieck introduced the concept in the early 1950s, following the work of Dunford and Pettis, who developed earlier results of Shizuo Kakutani, Kōsaku Yosida, and several others. Important results were obtained more recently by Jean Bourgain. Nevertheless, the Dunford–Pettis property is not completely understood. (en)
dcterms:subject	Banach spaces
Wikipage page ID	16388109 (xsd:integer)
Wikipage revision ID	1021681327 (xsd:integer)
Link from a Wikipage to another Wikipage	Banach spaces Uniform norm Kōsaku Yosida Compact space Continuous function Rocky Mountain Journal of Mathematics Lp space Shizuo Kakutani Compact operator Functional analysis Measure space Banach space Weak topology Alexander Grothendieck Dual space Dunford Hilbert space Jean Bourgain Nelson Dunford Sequence (mathematics) B. J. Pettis Reflexive Banach space Compact Hausdorff space Completely continuous
Link from a Wikipage to an external page	http://rmmc.asu.edu/abstracts/rmj/vol27-4/nrandpag1.pdf%7Cdoi-access=free https://books.google.com/books%3Fid=WahnFICUx1AC&pg=PA331%7Coclc=226084233
sameAs	Dunford–Pettis property Dunford–Pettis property Dunford–Pettis property Dunford–Pettis property
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Harv dbt:Functional_analysis
author	JMF Castillo, SY Shaw (en)
id	D/d110240 (en)
title	Dunford–Pettis property (en)
has abstract	Die Dunford-Pettis-Eigenschaft (nach N. Dunford und B. J. Pettis) ist eine im mathematischen Teilgebiet der Funktionalanalysis betrachtete Eigenschaft von Banachräumen. (de) In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C(K) of continuous functions on a compact space and the space L1(μ) of the Lebesgue integrable functions on a measure space. Alexander Grothendieck introduced the concept in the early 1950s, following the work of Dunford and Pettis, who developed earlier results of Shizuo Kakutani, Kōsaku Yosida, and several others. Important results were obtained more recently by Jean Bourgain. Nevertheless, the Dunford–Pettis property is not completely understood. (en)
gold:hypernym	Property
prov:wasDerivedFrom	wikipedia-en:Dunford–Pettis_property?oldid=1021681327&ns=0
page length (characters) of wiki page	4028 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Dunford–Pettis_property
is Link from a Wikipage to another Wikipage of	List of Brown University alumni Alexander Grothendieck Billy James Pettis Dunford-Pettis property Dunford (surname) Nelson Dunford
is Wikipage redirect of	Dunford-Pettis property
is foaf:primaryTopic of	wikipedia-en:Dunford–Pettis_property

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