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Hahn–Banach theorem

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem also shows that there are sufficient continuous linear functionals defined on every normed vector space in order to study the dual space. Another…

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Overview

History

Hahn–Banach theorem

Continuous extension theorem

Geometric Hahn–Banach (the Hahn–Banach separation theorems)

Applications

Generalizations

Converse

Relation to axiom of choice and other theorems

Bibliography

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Hahn–Banach theorem

Nodes151
Edges150
Triples343
Avg. degree1.99
Density0.013245
Components1

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Hahn–Banach theorem

Top relations

related to Bibliography · 182
Hahn–Banach theorem → Academic Press, Adasch, Advanced Courses, Albert, Alex, Alexander, American Mathematical Society, An, An Equivariant Version, Analysis, Applications, Applied Functional Analysis, Applied Mathematics, Archived, Banach, Banach Theorem, Barry, Beckenstein, Berberian, Berlin
related to Relation to axiom of choice and other theorems · 19
Hahn–Banach theorem → AC, Alaoglu, Although, Banach, Boolean, BPI, Fraenkel, Hahn, HB, However, It, Luxemburg, Ryll-Nardzewski, The, The Hahn, UL, Zermelo, ZF, Zorn's
related to Non-locally convex spaces · 15
Hahn–Banach theorem → Banach, Euclidean, F-space, For, Hahn, Hausdorff, However, If, Lebesgue, Riesz's, Rudin, Since, Specifically, The, TVS
related to history · 13
Hahn–Banach theorem → Banach, Eduard Helly, Hahn, Hahn's, Hans Hahn, Helly, Helly's, In, Marcel Riesz, Riesz, Stefan Banach, The, Whereas Helly's
see also · 11
Hahn–Banach theorem → Banach, Farkas, Hahn, Linear Fnctions, Mathematical, On, Positive Extensions, Real VectorspaceSeparating, Riesz, Solvability, Theorem
related to Converse · 10
Hahn–Banach theorem → Banach, For, Hahn, Hausdorff, HBEP, Kalton, Let, On, The Hahn, TVS
related to Geometric Hahn–Banach (the Hahn–Banach separation theorems) · 10
Hahn–Banach theorem → Banach, Hahn, If Int, Int, Lemmas, Let, The, Theorem, They, This
related to Example from Fredholm theory · 8
Hahn–Banach theorem → Banach, Hahn, Hausdorff, Proposition, Suppose, Then, To, TVS
related to Partial differential equations · 8
Hahn–Banach theorem → At, Banach, Hahn, If, Pu, Suppose, The, The Hahn
related to For seminorms · 7
Hahn–Banach theorem → Banach, Because, Hahn, If, Let, Minkowski, Then

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Important terminology

displaystyle linear theorem functional banach vector hahn continuous space leq extension convex real mathbb seminorm defined subspace spaces function exists

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hahn–Banach theoremis acentral result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space0.90text
Hahn–Banach theoremis afirst sign of an important philosophy in functional analysis0.90text
the moment probleminstance ofThis is needed to solve problems0.80text
whereby given all the potential moments of a function one must determine if a function having these moments existsinstance ofThis is needed to solve problems0.80text
andinstance ofThis is needed to solve problems0.80text
if soinstance ofThis is needed to solve problems0.80text
find it in terms of those momentsinstance ofThis is needed to solve problems0.80text
Hahn–Banach theoremhas applicationThe Hahn0.60section
Hahn–Banach theoremhas applicationBanach0.60section
Hahn–Banach theoremhas applicationFor0.60section
Hahn–Banach theoremhas applicationTo0.60section
Hahn–Banach theoremhas applicationMoreover0.60section

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