Kadison常数的正性与非对易Bloch理论
On positivity of the Kadison constant and noncommutative Bloch theory
摘要：
在以前的文章中，我们建立了Baum-Connes猜想和非交换Bloch理论之间的自然联系，即覆盖空间上射影周期椭圆算子的谱理论。我们详细阐述了这种联系，并提供了重要的证据，主猜测在非交换布洛赫理论的康托尔集型谱的不存在。这是通过建立一个明确的下界的Kadison常数的扭曲群C*-代数在大量的情况下，只要乘数是合理的。
英文摘要：
In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in noncommutative Bloch theory on the non-existence of Cantor set type spectrum. This is accomplished by establishing an explicit lower bound for the Kadison constant of twisted group C*-algebras in a large number of cases, whenever the multiplier is rational.
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