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Projectionless algebra : ウィキペディア英語版 | Projectionless algebra In mathematics, a projectionless C *-algebra is a C *-algebra with no projections besides 0 and 1. The problem of whether simple infinite dimensional C *-algebras with this property exist was posed in 1958 by Irving Kaplansky,〔.〕 and the first example of one was published in 1981 by Bruce Blackadar.〔〔.〕 Today other examples are available, such as the reduced group C *-algebra of the free group on finitely many generators.〔.〕 ==Examples==
* C, the complex numbers * Function spaces C0((0, 1)) and C((1 )). Note that the first only has 0 as a projection. If K is a compact Hausdorff space, then C(K) is a projectionless algebra if and only if K is connected.
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「Projectionless algebra」の詳細全文を読む
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