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Winter 2019 Semicircular-like and semicircular laws on Banach $*$-probability spaces induced by dynamical systems of the finite adele ring $A_{\Bbb{Q}}$
Ilwoo Cho
Adv. Oper. Theory 4(1): 24-70 (Winter 2019). DOI: 10.15352/aot.1802-1317

Abstract

Starting from the finite adele ring $A_{\Bbb{Q}},$ we construct semigroup dynamical systems of $A_{\Bbb{Q}},$ acting on certain $C^{*}$-probability spaces. From such dynamical-systematic $C^{*}$-probability spaces, we construct Banach-space operators acting on the $C^{*}$-probability spaces and corresponding Banach $*$-probability spaces. In particular, we are interested in Banach-space operators whose free distributions are the (weighted-)semicircular law(s).

Citation

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Ilwoo Cho. "Semicircular-like and semicircular laws on Banach $*$-probability spaces induced by dynamical systems of the finite adele ring $A_{\Bbb{Q}}$." Adv. Oper. Theory 4 (1) 24 - 70, Winter 2019. https://doi.org/10.15352/aot.1802-1317

Information

Received: 16 February 2018; Accepted: 12 March 2018; Published: Winter 2019
First available in Project Euclid: 4 April 2018

zbMATH: 06946443
MathSciNet: MR3867334
Digital Object Identifier: 10.15352/aot.1802-1317

Subjects:
Primary: 47L30
Secondary: 11R47, 11R56, 46L54, 47L55

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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