论文标题
在Quaternionic Essential数值范围内
On the convexity of the quaternionic essential numerical range
论文作者
论文摘要
通常，季度设置中的数值范围是四季度的非凸子集。基本数值范围是对数值范围的改进，后者仅保留具有一定意义上无限多重性的元素。我们证明了Quaternionic Hilbert空间上有界线性算子的基本数值范围是凸。还提供了兰开斯特定理的四元素类似物，该类似物还提供了数值范围及其必需数值范围的关闭。
The numerical range in the quaternionic setting is, in general, a non convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert space is convex. A quaternionic analogue of Lancaster theorem, relating the closure of the numerical range and its essential numerical range, is also provided.
