论四元基本数值范围的凸性

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-05-15 DOI:10.1017/s0013091524000336

LuÍs Carvalho, Cristina Diogo, Sérgio Mendes, Helena Soares

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引用次数: 0

摘要

一般来说，四元数环境中的数值范围是四元数的一个非凸子集。本质数值范围是数值范围的细化，只保留在某种意义上具有无限倍性的元素。我们证明了四元数希尔伯特空间上有界线性算子的基本数值范围是凸的。我们还提供了兰卡斯特定理的四元数类似定理，它涉及数值范围的闭合及其基本数值范围。

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On the convexity of the quaternionic essential numerical range

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.

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来源期刊

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.