Operators induced by certain hypercomplex systems

• Autorzy: Alpay Daniel , Cho Ilwoo

Identyfikatory

DOI

10.7494/OpMath.2023.43.3.275

• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider a family {Ht}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, πt)} t∈R of the hypercomplex system {Ht}t∈R, and study the realizations πt(h) of hypercomplex numbers h ∈ Ht, 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.

Słowa kluczowe

EN

scaled hypercomplex ring; scaled hypercomplex monoids; representations; scaled-spectral forms; scaled-spectralization

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 3
• Strony: 275--333
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Alpay Daniel

• Chapman University, Department of Mathematics, One University Dr., Orange, CA 92866, U.S.A.

• https://orcid.org/0000-0002-7612-3598

autor

Cho Ilwoo

• Saint Ambrose University, Department of Mathematics and Statistics, 518 W. Locust St., Davenport, IA 52803, U.S.A.

• https://orcid.org/0000-0001-8962-1089

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)