About: Mackey–Arens theorem

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

The Mackey–Arens theorem is an important theorem in functional analysis that characterizes those locally convex vector topologies that have some given space of linear functionals as their continuous dual space. According to Narici (2011), this profound result is central to duality theory; a theory that is "the central part of the modern theory of topological vector spaces."

Property	Value
dbo:abstract	The Mackey–Arens theorem is an important theorem in functional analysis that characterizes those locally convex vector topologies that have some given space of linear functionals as their continuous dual space. According to Narici (2011), this profound result is central to duality theory; a theory that is "the central part of the modern theory of topological vector spaces." (en)
dbo:wikiPageID	29072525 (xsd:integer)
dbo:wikiPageLength	4220 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID	1108337993 (xsd:integer)
dbo:wikiPageWikiLink	dbc:Lemmas dbc:Topological_vector_spaces dbr:Continuous_dual_space dbr:Functional_analysis dbr:Mackey_topology dbr:Topological_vector_space dbr:Dual_system dbr:Linear_functional dbc:Functional_analysis dbr:Polar_topology dbr:Locally_convex dbr:Separating_set
dbp:mathStatement	Let X be a vector space and let 𝒯 be a locally convex Hausdorff topological vector space topology on X. Let denote the continuous dual space of X and let denote X with the topology 𝒯. Then the following are equivalent: And furthermore, (en)
dbp:name	Mackey–Arens theorem (en)
dbp:wikiPageUsesTemplate	dbt:' dbt:Big dbt:Main dbt:Math dbt:Mvar dbt:Ordered_list dbt:Reflist dbt:Sfn dbt:Functional_analysis dbt:Math_theorem dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Rudin_Walter_Functional_Analysis dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Topological_vector_spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Duality_and_spaces_of_linear_maps
dcterms:subject	dbc:Lemmas dbc:Topological_vector_spaces dbc:Functional_analysis
rdfs:comment	The Mackey–Arens theorem is an important theorem in functional analysis that characterizes those locally convex vector topologies that have some given space of linear functionals as their continuous dual space. According to Narici (2011), this profound result is central to duality theory; a theory that is "the central part of the modern theory of topological vector spaces." (en)
rdfs:label	Mackey–Arens theorem (en)
owl:sameAs	wikidata:Mackey–Arens theorem https://global.dbpedia.org/id/FWgbB
prov:wasDerivedFrom	wikipedia-en:Mackey–Arens_theorem?oldid=1108337993&ns=0
foaf:isPrimaryTopicOf	wikipedia-en:Mackey–Arens_theorem
is dbo:wikiPageWikiLink of	dbr:List_of_functional_analysis_topics dbr:George_Mackey dbr:Mackey_topology dbr:Polar_topology dbr:Richard_Friederich_Arens
is dbp:knownFor of	dbr:George_Mackey
is foaf:primaryTopic of	wikipedia-en:Mackey–Arens_theorem