About: Vector-valued Hahn–Banach theorems

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In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued in the real numbers or the complex numbers ) to linear operators valued in topological vector spaces (TVSs).

Attributes	Values
rdfs:label	Vector-valued Hahn–Banach theorems (en)
rdfs:comment	In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued in the real numbers or the complex numbers ) to linear operators valued in topological vector spaces (TVSs). (en)
name	Theorem (en)
dcterms:subject	Topological vector spaces
Wikipage page ID	64514712 (xsd:integer)
Wikipage revision ID	1088252225 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Topological vector spaces Complete topological vector space Complex number Operator norm Separable space Locally convex topological vector space Lp space Functional analysis Banach space Topological vector space Hausdorff space Alexander Grothendieck Normed space Projection (linear algebra) Hahn–Banach theorem Hilbert space Archimedean ordered Real number Reflexive space Locally convex Extremally disconnected space Vector lattice Identity map
sameAs	Vector-valued Hahn–Banach theorems Vector-valued Hahn–Banach theorems
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has abstract	In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued in the real numbers or the complex numbers ) to linear operators valued in topological vector spaces (TVSs). (en)
math statement	Suppose that is a Banach space over the field Then the following are equivalent: # is 1-injective; # has the metric extension property; # has the immediate 1-extension property; # has the center-radius property; # has the weak intersection property; # is 1-complemented in any Banach space into which it is norm embedded; # Whenever in norm-embedded into a Banach space then identity map can be extended to a continuous linear map of norm to ; # is linearly isometric to for some compact, Hausdorff space, extremally disconnected space . . where if in addition, is a vector space over the real numbers then we may add to this list: # has the binary intersection property; # is linearly isometric to a complete Archimedean ordered vector lattice with order unit and endowed with the order unit norm. (en) Suppose that is a Banach space with the metric extension property. Then the following are equivalent: # is reflexive; # is separable; # is finite-dimensional; # is linearly isometric to for some discrete finite space (en)
prov:wasDerivedFrom	wikipedia-en:Vector-valued_Hahn–Banach_theorems?oldid=1088252225&ns=0
page length (characters) of wiki page	8756 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Vector-valued_Hahn–Banach_theorems
is rdfs:seeAlso of	Hahn–Banach theorem
is Link from a Wikipage to another Wikipage of	Vector-Valued Hahn-Banach theorems Vector-valued Hahn-Banach theorems
is Wikipage redirect of	Vector-Valued Hahn-Banach theorems Vector-valued Hahn-Banach theorems
is foaf:primaryTopic of	wikipedia-en:Vector-valued_Hahn–Banach_theorems

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