| 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) |
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29072525 (xsd:integer) |
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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) |
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| 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) |
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wikidata:Mackey–Arens theorem https://global.dbpedia.org/id/FWgbB |
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wikipedia-en:Mackey–Arens_theorem?oldid=1108337993&ns=0 |
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wikipedia-en:Mackey–Arens_theorem |
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dbr:List_of_functional_analysis_topics dbr:George_Mackey dbr:Mackey_topology dbr:Polar_topology dbr:Richard_Friederich_Arens |
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dbr:George_Mackey |
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wikipedia-en:Mackey–Arens_theorem |