拟中心模与自相似集：Voiculescu工作的补充结果
Quasicentral modulus and self-similar sets: a supplementary result to Voiculescu's work
摘要：
在他最近的工作中，Voiculescu将他关于$(n,1)$ -Lorentz理想的交换$n$ -元组的拟中心模的公式推广到其谱包含在某类Cantor类自相似集中的情况。本文讨论了满足开集条件的一般自相似集，得到了拟中心模的上下上界。我们的证明表明，Voiculescu的公式适用于一类自相似集，包括Sierpinski垫片和Sierpinski地毯。
英文摘要：
In his recent work, Voiculescu generalized his remarkable formula for the quasicentral modulus of a commuting $n$-tuple of hermitian operators with respect to the $(n,1)$-Lorentz ideal to the case where its spectrum is contained in a Cantor-like self-similar set in a certain class. In this note, we treat general self-similar sets satisfying the open set condition, and obtain lower and upper bounds of the quasicentral modulus. Our proof shows that Voiculescu's formula holds for a class of self-similar sets including the Sierpinski gasket and the Sierpinski carpet.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
