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1
Content available Deformation of semicircular and circular laws via p-adic number fields and sampling of primes
Cho Ilwoo, Jorgensen Palie E. T.
Opuscula Mathematica
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2019
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Vol. 39, no. 6
773--813
EN
In this paper, we study semicircular elements and circular elements in a certain Banach *-probability space [formula] induced by analysis on the p-adic number fields Qp over primes p. In particular, by truncating the set P of all primes for given suitable real numbers t < s in R, two different types of truncated linear functionals [formula], and [formula] re constructed on the Banach *-algebra [formula]. We show how original free distributional data (with respect to r°) are distorted by the truncations on P (with respect to [formula], and [formula]). As application, distorted free distributions of the semicircular law, and those of the circular law are characterized up to truncation.
2
Content available Adelic analysis and functional analysis on the finite Adele ring
Cho I.
Opuscula Mathematica
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2018
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Vol. 38, no. 2
139--185
EN
In this paper, we study operator theory on the *-algebra Mp, consisting of all measurable functions on the finite Adele ring Aq, in extended free-probabilistic sense. Even though our *-algebra Mp is commutative, our Adelic-analytic data and properties on Mv 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 Aq, we construct the suitable Hilbert-space representation, and study a C*-algebra M-p generated by M-p under representation. In particular, we focus on operator-theoretic properties of certain generating operators on Mp.
3
Content available On dynamical systems induced by p-adic number fields
Cho I.
Opuscula Mathematica
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2015
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Vol. 35, no. 4
445--484
EN
In this paper, we construct dynamical systems induced by p-adic number fields Qp. 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.
4
Content available p-adic Banach space operators and adelic Banach space operators
Cho I.
Opuscula Mathematica
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2014
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Vol. 34, no. 1
29--65
EN
In this paper, we study non-Archimedean Banach *-algebras Mp over the p-adic number fields Qp, and MQ over the adele ring AQ. We call elements of Mp, p-adic operators, for all primes p, respectively, call those of MQ, adelic operators. We characterize MQ in terms of Mp’s. Based on such a structure theorem of MQ, we introduce some interesting p-adic operators and adelic operators
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