TY  - JOUR
ID  - Cho2017
LB  - Cho2017
AU  - Cho, Ilwoo
AU  - Jorgensen, Palle E. T.
TI  - Semicircular elements induced by p-adic number fields
ST  - Semicircular elements induced by p-adic number fields
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 5
SP  - 665
EP  - 703
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.5.665
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.5.665
AB  - 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 \(\mathbb{Q}_{p}\), we construct a Banach \(*\)-algebra \(\mathfrak{LS}_{p}\), for a fixed prime \(p\), and show the generating elements \(Q_{p,j}\) of \(\mathfrak{LS}_{p}\) form weighted-semicircular elements, and the corresponding scalar-multiples \(\Theta_{p,j}\) of \(Q_{p,j}\) become semicircular elements, for all \(j\in\mathbb{Z}\). The main result of this paper is the very construction of suitable linear functionals \(\tau_{p,j}^{0}\) on \(\mathfrak{LS}_{p}\), making \(Q_{p,j}\) be weighted-semicircular, for all \(j\in\mathbb{Z}\).
KW  - free probability
KW  - primes
KW  - \(p\)-adic number fields \(\mathbb{Q}_{p}\)
KW  - Hilbert-space representations
KW  - \(C^{*}\)-algebras
KW  - wighted-semicircular elements
KW  - semicircular elements
SN  - 1232-9274
ER  -