About: L-infinity

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In mathematics, , the (real or complex) vector space of bounded sequences with the supremum norm, and , the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former is a special case of the latter. As a Banach space they are the continuous dual of the Banach spaces of absolutely summable sequences, and of absolutely integrable measurable functions (if the measure space fulfills the conditions of being localizable and therefore semifinite). Pointwise multiplication gives them the structure of a Banach algebra, and in fact they are the standard examples of abelian Von Neumann algebras.

Attributes	Values
rdfs:label	L∞-Raum (de) Espace L∞ (fr) L-infinity (en)
rdfs:comment	En mathématiques, l'espace L∞ est un des espaces classiques de l'analyse fonctionnelle. Il est constitué de fonctions mesurables bornées, modulo la relation d'égalité presque partout. Il s'agit d'un espace de Banach qui vient s'ajouter à la famille des espaces Lp de fonctions mesurables dont la puissance p-ième est intégrable. C'est même une algèbre de Banach commutative unifère. (fr) In mathematics, , the (real or complex) vector space of bounded sequences with the supremum norm, and , the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former is a special case of the latter. As a Banach space they are the continuous dual of the Banach spaces of absolutely summable sequences, and of absolutely integrable measurable functions (if the measure space fulfills the conditions of being localizable and therefore semifinite). Pointwise multiplication gives them the structure of a Banach algebra, and in fact they are the standard examples of abelian Von Neumann algebras. (en)
dcterms:subject	Banach spaces Function spaces Normed spaces
Wikipage page ID	46395425 (xsd:integer)
Wikipage revision ID	1083547639 (xsd:integer)
Link from a Wikipage to another Wikipage	Bounded sequence Banach spaces Function spaces Vector space Von Neumann algebra Mathematics Lp space Function space Measure space Banach space Economies Essential infimum and essential supremum Banach algebra Normed spaces Supremum Sequence space Consumption set Reflexive Banach space Essentially bounded
sameAs	L-infinity L-infinity L-infinity L-infinity L-infinity L-infinity
dbp:wikiPageUsesTemplate	dbt:Banach_spaces dbt:About dbt:Annotated_link dbt:Multiple_issues dbt:Refimprove dbt:Reflist dbt:Short_description dbt:Technical dbt:Functional_analysis
has abstract	En mathématiques, l'espace L∞ est un des espaces classiques de l'analyse fonctionnelle. Il est constitué de fonctions mesurables bornées, modulo la relation d'égalité presque partout. Il s'agit d'un espace de Banach qui vient s'ajouter à la famille des espaces Lp de fonctions mesurables dont la puissance p-ième est intégrable. C'est même une algèbre de Banach commutative unifère. (fr) In mathematics, , the (real or complex) vector space of bounded sequences with the supremum norm, and , the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former is a special case of the latter. As a Banach space they are the continuous dual of the Banach spaces of absolutely summable sequences, and of absolutely integrable measurable functions (if the measure space fulfills the conditions of being localizable and therefore semifinite). Pointwise multiplication gives them the structure of a Banach algebra, and in fact they are the standard examples of abelian Von Neumann algebras. (en)
prov:wasDerivedFrom	wikipedia-en:L-infinity?oldid=1083547639&ns=0
page length (characters) of wiki page	4860 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:L-infinity
is Link from a Wikipage to another Wikipage of	Debreu theorems Covering number Lp space Product (category theory) L-infinity-space
is Wikipage redirect of	L-infinity-space
is foaf:primaryTopic of	wikipedia-en:L-infinity

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