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Banach–Alaoglu theorem

In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. A common proof identifies the unit ball with the weak-* topology as a closed subset of a product of compact sets with the…

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History

Statement

Sequential Banach–Alaoglu theorem

Consequences

Relation to the axiom of choice and other statements

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Banach–Alaoglu theorem

Nodes106
Edges105
Triples62
Avg. degree1.98
Density0.018868
Components1

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Banach–Alaoglu theorem

Top relations

related to Relation to the axiom of choice and other statements · 15
Banach–Alaoglu theorem → Alaoglu, Banach, Fraenkel, Hahn, Hausdorff, HB, However, In, Lemma, Most, The Banach, Tychonoff's, Zermelo, ZF, ZFC
related to Consequences for normed spaces · 14
Banach–Alaoglu theorem → Alaoglu, Assume, Banach, Eberlein, For, If, James, Let, Lp, Riesz's, So, The, Then, This
related to history · 14
Banach–Alaoglu theorem → According, Alaoglu, Banach, Bourbaki, Edward Beckenstein, Helly, In, Lawrence Narici, Leonidas Alaoglu, Pietsch, Stefan Banach, The, The Bourbaki, This
related to Sequential Banach–Alaoglu theorem · 9
Banach–Alaoglu theorem → Alaoglu, Arzelà, Ascoli, Banach, In, Sequential, Since, Specifically, Then
related to Elementary proof · 8
Banach–Alaoglu theorem → Alaoglu, Also, An, Banach, Cartesian, The, Unlike, What
is a · 1
Banach–Alaoglu theorem → sequential version of the theorem

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Important terminology

displaystyle closed space compact theorem left right prime topology banach dual alaoglu subset weak- ball also proof unit sigma vector

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Banach–Alaoglu theoremis asequential version of the theorem0.90text
the algebraic dual space Xinstance ofand subspace topologies they induce on subsets0.80text
Banach–Alaoglu theoremrelated to Consequences for normed spacesAssume0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesThe0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesSo0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesRiesz's0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesBanach0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesJames0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesIf0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesThis0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesAlaoglu0.60section
Banach–Alaoglu theoremrelated to Consequences for normed spacesEberlein0.60section

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