Operators Induced by Certain Hypercomplex Systems

Authors

Daniel Alpay, Chapman UniversityFollow
Ilwoo Choo, St. Ambrose UniversityFollow

Document Type

Article

Publication Date

5-17-2023

Abstract

In this paper, we consider a family {H_t}_t∈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 {(C², π_t)}_t∈R of the hypercomplex system {H_t}_t∈R, and study the realizations π_t(h) of hypercomplex numbers h ∈ H_t, as (2 × 2)-matrices acting on C², for an arbitrarily fixed scale t ∈ R. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.

Comments

This article was originally published in Opuscula Mathematica, volume 43, issue 3, in 2023. https://doi.org/10.7494/OpMath.2023.43.3.275

Recommended Citation

Daniel Alpay, Ilwoo Cho, Operators induced by certain hypercomplex systems, Opuscula Math. 43, no. 3 (2023), 275-333, https://doi.org/10.7494/OpMath.2023.43.3.275

Peer Reviewed

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This work is licensed under a Creative Commons Attribution 4.0 License.