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arXiv · 2301.08720

Operators induced by certain hypercomplex systems

Daniel Alpay·Ilwoo Cho
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Abstract

In this paper, we consider natural Hilbert-space representations $\left\{ \left(\mathbb{C}^{2},\pi_{t}\right)\right\} _{t\in\mathbb{R}}$ of the hypercomplex system $\left\{ \mathbb{H}_{t}\right\} _{t\in\mathbb{R}}$, and study the realizations $\pi_{t}\left(h\right)$ of hypercomplex numbers $h\in\mathbb{H}_{t}$, as $\left(2\times2\right)$-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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Daniel Alpay, Ilwoo Cho. 2023-01-20. Operators induced by certain hypercomplex systems. https://arxiv.org/abs/2301.08720

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