Nuclear dimension and sums of commutators
Nuclear dimension and sums of commutators
复制标题
核维数和换向器之和
DOI：
10.1512/iumj.2015.64.5472
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
L. Robert
中科院分区：
文献类型：
--
作者：
L. Robert
在有限核维数的C ~*-代数的背景下，研究了将在所有有界迹上为零的自伴元表示为有限个和（或和的极限）的问题.上界-在核维度的C*-代数-给出了在这些和所需的recruitors的数量。一个例子给出了一个简单的，核C*-代数（无限核维）与一个独特的tracial状态和元素，消失在所有有界的痕迹，但“严重”近似的有限总和的recruitators。最后，同样的问题进行了研究（可能是非核）简单的单位C*-代数假设适当的正则性在其Cuntz半群。
The problem of expressing a selfadjoint element that is zero on every bounded trace as a finite sum (or a limit of sums) of commutators is investigated in the setting of C*-algebras of finite nuclear dimension. Upper bounds -- in terms of the nuclear dimension of the C*-algebra -- are given for the number of commutators needed in these sums. An example is given of a simple, nuclear C*-algebra (of infinite nuclear dimension) with a unique tracial state and with elements that vanish on all bounded traces and yet are "badly" approximated by finite sums of commutators. Finally, the same problem is investigated on (possibly non-nuclear) simple unital C*-algebras assuming suitable regularity properties in their Cuntz semigroups.