论文标题
寻找凸：对角线和数值范围
In search of convexity: diagonals and numerical ranges
论文作者
论文摘要
我们表明，有界希尔伯特空间操作员的所有可能恒定对角线的集合始终是凸。特别是，这回答了J.-C。的一个公开问题。布林（$ 2003 $）。此外，我们表明，通勤操作员元组的关节数值范围通常不是凸，这填补了文献中的空白。我们还证明，asplund-ptak数值范围（对于成对的运算符）通常不是用于操作员元素的凸。
We show that the set of all possible constant diagonals of a bounded Hilbert space operator is always convex. This, in particular, answers an open question of J.-C. Bourin ($2003$). Moreover, we show that the joint numerical range of a commuting operator tuple is in general not convex, which fills a gap in the literature. We also prove that the Asplund-Ptak numerical range (which is convex for pairs of operators) is, in general, not convex for tuples of operators.
