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Continuous linear extension

In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space X {\displaystyle X} by first defining a linear transformation L {\displaystyle L} on a dense subset of X {\displaystyle X} and then continuously extending L {\displaystyle L} to the whole space via the theorem below. The resulting extension…

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Theorem

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The Hahn–Banach theorem

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Continuous linear extension

Nodes27
Edges26
Triples0
Avg. degree1.93
Density0.074074
Components1

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displaystyle linear theorem bounded extension continuous dense transformation space mathcal vector widehat function functional analysis normed hahn banach complete subset

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