- Tytuł:
- Operators induced by certain hypercomplex systems
- Autorzy:
-
Alpay, Daniel
Cho, Ilwoo - Powiązania:
- https://bibliotekanauki.pl/articles/29519364.pdf
- Data publikacji:
- 2023
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
scaled hypercomplex ring
scaled hypercomplex monoids
representations
scaled-spectral forms
scaled-spectralization - Opis:
- In this paper, we consider a family $ { \mathbb{H}_t }_{t∈\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, π_t)}_{t∈\mathbb{R} } $ of the hypercomplex system $ {\mathbb{H}_t }_{t∈\mathbb{R} } $, and study the realizations $ π_t (h) $ of hypercomplex numbers $ h ∈ \mathbb{H}_t $, as (2 × 2)-matrices acting on $ \mathbb{C}^2 $, for an arbitrarily fixed scale $ t ∈ \mathbb{R} $. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
- Źródło:
-
Opuscula Mathematica; 2023, 43, 3; 275-333
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł