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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. ==Theorem== Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation is iff the norm of is . This theorem is sometimes called the B L T theorem, where B L T stands for ''bounded linear transformation''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「continuous linear extension」の詳細全文を読む スポンサード リンク
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