某些超复系统诱导的算子

IF 1 Q1 MATHEMATICS
D. Alpay, Ilwoo Cho
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引用次数: 3

摘要

在本文中,我们考虑一个族\(\{\mathbb{H}_{t} \}_{t\in\mathbb{R}}\)的超复数环,由实数索引,包含四元数和分裂四元数。我们考虑超复形系统的自然Hilbert空间表示\(\{\mathbb{C}^{2},\ pi_{t})\}_{t\in\mathbb{R}}){H}_{t} 研究了超复数\(h\in\mathbb{H}_{t} \),作为\((2\乘2)\)-作用于\(\mathbb{C}^{2}\)的矩阵,对于任意固定的标度\(t\in\mathbb{R})。考虑了它们的代数性质、算子理论性质、谱分析性质和自由概率性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Operators induced by certain hypercomplex systems
In this paper, we consider a family \(\{ \mathbb{H}_{t}\}_{t\in\mathbb{R}}\) of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations \(\{(\mathbb{C}^{2},\pi_{t})\}_{t\in\mathbb{R}}\) of the hypercomplex system \(\{ \mathbb{H}_{t}\}_{t\in\mathbb{R}}\), and study the realizations \(\pi_{t}(h)\) of hypercomplex numbers \(h \in \mathbb{H}_{t}\), as \((2\times 2)\)-matrices acting on \(\mathbb{C}^{2}\), for an arbitrarily fixed scale \(t\in\mathbb{R}\). Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
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来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
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