论文标题
Crouzeix的猜想和相关问题
Crouzeix's Conjecture and related problems
论文作者
论文摘要
在本文中，我们建立了与Crouzeix的猜想有关的几个结果。我们表明，猜想与足够完善的特征值有关。这种分离是通过所谓的分离常数来衡量的，该常数是根据伪血脂指标定义的。此外，我们研究了相关的极端功能和相关向量的一般特性。在整个过程中，班次的压缩是说明示例的说明，这也允许进行精致的结果。
In this paper, we establish several results related to Crouzeix's conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined results.
