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.

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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. (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)
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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. (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)
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  • Continuous linear extension (en)
  • 連続線型拡張 (ja)
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