PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 9

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Banach *-algebras generated by semicircular elements induced by certain orthogonal projections
Cho I., Jorgensen P. E. T.
Opuscula Mathematica
|
2018
|
Vol. 38, no. 4
501--535
EN
The main purpose of this paper is to study structure theorems of Banach *-algebras generated by semicircular elements. In particular, we are interested in the cases where given semicircular elements are induced by orthogonal projections in a C*-probability space.
2
Content available Adelic analysis and functional analysis on the finite Adele ring
Cho I.
Opuscula Mathematica
|
2018
|
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 Semicircular elements induced by p-adic number fields
Cho I., Jorgensen P. E. T.
Opuscula Mathematica
|
2017
|
Vol. 37, no. 5
665--703
EN
In this paper, we study semicircular-like elements, and semicircular elements induced by p-adic analysis, for each prime p. Starting from a p-adic number field Qp, we construct a Banach *-algebra [formula], for a fixed prime p, and show the generating elements Qpj of [formula] form weighted-semicircular elements, and the corresponding scalar-multiples Θpj of Qpj become semicircular elements, for all j ∈ Z. The main result of this paper is the very construction of suitable linear functionals [formula] on [formula], making Qpj be weighted-semicircular, for all j ∈ Z.
4
Content available Non-factorizable c-valued functions induced by finite connected graphs
Cho I.
Opuscula Mathematica
|
2017
|
Vol. 37, no. 2
225--263
EN
In this paper, we study factorizability of C-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) “non-factorizability” of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function.
5
Content available Free probability on Hecke algebras and certain group C*-algebras induced by Hecke algebras
Cho I.
Opuscula Mathematica
|
2016
|
Vol. 36, no. 2
153--187
EN
In this paper, by establishing free-probabilistic models on the Hecke algebras [formula] induced by p-adic number fields Qp, we construct free probability spaces for all primes p. Hilbert-space representations are induced by such free-probabilistic structures. We study C*-algebras induced by certain partial isometries realized under the representations.
6
Content available Certain group dynamical systems induced by Hecke algebras
Cho I.
Opuscula Mathematica
|
2016
|
Vol. 36, no. 3
337--373
EN
In this paper, we study dynamical systems induced by a certain group [formula] embedded in the Hecke algebra H(Gp) induced by the generalized linear group Gp = GL2(Qp) over the p-adic number fields Qp for a fixed prime p. We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms ol free probability on the Hecke algebra H(Gp).
7
Content available On dynamical systems induced by p-adic number fields
Cho I.
Opuscula Mathematica
|
2015
|
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.
8
Content available p-adic Banach space operators and adelic Banach space operators
Cho I.
Opuscula Mathematica
|
2014
|
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
9
Content available Free probability induced by electric resistance networks on energy Hilbert spaces
Cho I., Jorgensen P. E. T.
Opuscula Mathematica
|
2011
|
Vol. 31, no. 4
549-598
EN
We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs) are naturally associated with groupoids. Starting with a fixed ERN, it is known that there is a canonical energy form and a derived energy Hilbert space Hε. From Hε, one then studies resistance metrics and boundaries of the ERNs. But in earlier research, there does not appear to be a natural algebra of bounded operators acting on Hε. With the use of our ERN-groupoid, we show that Hε may be derived as a representation Hilbert space of a universal representation of a groupoid algebra [formula], and we display other representations. Among our applications, we identify a free structure of [formula] in terms of the energy form.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.