About: Continuous linear extension

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In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below. The resulting extension remains linear and bounded (thus continuous). This procedure is known as continuous linear extension.

Attributes	Values
rdfs:label	Continuous linear extension (en) 連続線型拡張 (ja)
rdfs:comment	In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below. The resulting extension remains linear and bounded (thus continuous). This procedure is known as continuous linear extension. (en) 数学の関数解析学の分野における連続線型拡張（れんぞくせんけいかくちょう、英: continuous linear extension）とは、次に述べる手順のことを指す：完備なノルム線型空間上にある線型変換を定義する時、初めに内の稠密な部分集合上に線型変換を定義し、その後、後述の定理によって、を全空間へと拡張することが便利となることが、しばしばある。この結果として得られる拡張は線型かつ有界（したがって、連続）である。 (ja)
dcterms:subject	Functional analysis
Wikipage page ID	460637 (xsd:integer)
Wikipage revision ID	1099053261 (xsd:integer)
Link from a Wikipage to another Wikipage	Riemann integral Complete space Continuous function Operator norm Bounded operator Lp space Closure (mathematics) Dense set Functional analysis Step function Linear map Hahn–Banach theorem Interval (mathematics) Functional analysis If and only if Indicator function Linear transformation Existence Piecewise Normed vector space Subset
sameAs	Continuous linear extension Continuous linear extension Continuous linear extension Continuous linear extension
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Functional_Analysis dbt:TopologicalVectorSpaces
has abstract	In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below. The resulting extension remains linear and bounded (thus continuous). This procedure is known as continuous linear extension. (en) 数学の関数解析学の分野における連続線型拡張（れんぞくせんけいかくちょう、英: continuous linear extension）とは、次に述べる手順のことを指す：完備なノルム線型空間上にある線型変換を定義する時、初めに内の稠密な部分集合上に線型変換を定義し、その後、後述の定理によって、を全空間へと拡張することが便利となることが、しばしばある。この結果として得られる拡張は線型かつ有界（したがって、連続）である。 (ja)
prov:wasDerivedFrom	wikipedia-en:Continuous_linear_extension?oldid=1099053261&ns=0
page length (characters) of wiki page	4108 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Continuous_linear_extension
is Link from a Wikipage to another Wikipage of	BLT theorem List of functional analysis topics Oscillatory integral operator Dense set Itô calculus Tatyana Shaposhnikova Trace operator Regulated integral BLT-theorem Extension of an operator
is Wikipage redirect of	BLT theorem BLT-theorem Extension of an operator
is foaf:primaryTopic of	wikipedia-en:Continuous_linear_extension

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