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Abstract index group : ウィキペディア英語版 | Abstract index group In operator theory, every Banach algebra can be associated with a group called its abstract index group. == Definition == Let ''A'' be a Banach algebra and ''G'' the group of invertible elements in ''A''. The set ''G'' is open and a topological group. Consider the identity component :''G''0, or in other words the connected component containing the identity 1 of ''A''; ''G''0 is a normal subgroup of ''G''. The quotient group :Λ''A'' = ''G''/''G''0 is the abstract index group of ''A''. Because ''G''0, being the component of an open set, is both open and closed in ''G'', the index group is a discrete group.
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「Abstract index group」の詳細全文を読む
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