|
In mathematics, the real rank of a C *-algebra is a noncommutative analogue of Lebesgue covering dimension. == Definition == The definition was first introduced by Lawrence G. Brown and Gert K. Pedersen. The real rank of a unital C *-algebra ''A'' is the smallest non-negative integer ''n'', denoted RR(''A''), such that for every (''n'' + 1)-tuple (''x''0, ''x''1, ... ,''x''''n'') of self-adjoint elements of ''A'' and every ''ε'' > 0, there exists an (''n'' + 1)-tuple (''y''0, ''y''1, ... ,''y''''n'') of self-adjoint elements of ''A'' such that is invertible and . Nearly by definition, if ''X'' is a compact Hausdorff space, then RR(''C''(''X'')) = dim(''X''), where dim refers to the Lebesgue covering dimension of the space ''X''. 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「Real rank (C*-algebras)」の詳細全文を読む スポンサード リンク
|