Browsing by Subject "Adele ring"

Now showing 1 - 2 of 2

Access status: Open Access ,
Adelic analysis and functional analysis on the finite Adele ring
(Wydawnictwa AGH, 2018) Cho, Ilwoo
In this paper, we study operator theory on the $∗$-algebra $\mathcal{M}_{\mathcal{P}}$, consisting of all measurable functions on the finite Adele ring $A_{\mathbb{Q}}$, in extended free-probabilistic sense. Even though our $∗$-algebra $\mathcal{M}_{\mathcal{P}}$ is commutative, our Adelic-analytic data and properties on $\mathcal{M}_{\mathcal{P}}$ are understood as certain free-probabilistic results under enlarged sense of (noncommutative) free probability theory (well-covering commutative cases). From our free-probabilistic model on $A_{\mathbb{Q}}$, we construct the suitable Hilbert-space representation, and study a $C∗$-algebra $M_{\mathcal{P}}$ generated by $\mathcal{M}_{\mathcal{P}}$ under representation. In particular, we focus on operator-theoretic properties of certain generating operators on $M_{\mathcal{P}}$.
Access status: Open Access ,
On dynamical systems induced by p-adic number fields
(2015) Cho, Ilwoo
In this paper, we construct dynamical systems induced by $p$-adic number fields $\mathbb{Q}_{p}$. We study the corresponding crossed product operator algebras induced by such dynamical systems. In particular, we are interested in structure theorems, and free distributional data of elements in the operator algebras.