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Densely defined operator : ウィキペディア英語版 | Densely defined operator In mathematics — specifically, in operator theory — a densely defined operator or partially defined operator is a type of partially defined function. In a topological sense, it is a linear operator that is defined "almost everywhere". Densely defined operators often arise in functional analysis as operations that one would like to apply to a larger class of objects than those for which they ''a priori'' "make sense". ==Definition==
A densely defined linear operator ''T'' from one topological vector space, ''X'', to another one, ''Y'', is a linear operator that is defined on a dense linear subspace dom(''T'') of ''X'' and takes values in ''Y'', written ''T'' : dom(''T'') ⊆ ''X'' → ''Y''. Sometimes this is abbreviated as ''T'' : ''X'' → ''Y'' when the context makes it clear that ''X'' might not be the set-theoretic domain of ''T''.
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「Densely defined operator」の詳細全文を読む
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