On Dynamical Systems Induced by the Adele Ring

Ilwoo Cho

Authors

Ilwoo Cho

prime fields (or, p-adic number fields), the adele ring, p-adicvon neumann algebras, adele-ring von neumann algebras, p-adic dynamical systems, adelic

Abstract

In this paper, we construct a dynamical system induced by the Adele ring AQ ; based on the dynamical systems induced by -adic number fields p Qp ; for all primes : We study fundamental operator-theoretic and operator- p algebraic properties of the corresponding crossed product operator algebra generated by such a dynamical system, via free probability.

Downloads

How to Cite

On Dynamical Systems Induced by the Adele Ring. (2015). Global Journal of Science Frontier Research, 15(18), 35-67. https://journalofscience.org/index.php/GJSFR/article/view/

Download Citation

References

Arveson (2002) Preprint.

Arveson (2003) Springer. 0-387.

D. Bump (1996) Cambridge Univ. 0-521.

I. Cho, Operators Numbers, Methods Math (2013) Operators induced by prime numbers. 313-340.

I. Cho, p-Adic Operators, Opuscula Adelic Banach-Space Operators (2014) p-adic Banach space operators and adelic Banach space operators. 29.

I. Cho (2014) Dynamical Systems on Arithmetic Functions Determined by Primes. https://doi.org/10.15352/bjma/09-1-15(2014

I. Cho (2014) Free Distributional Data of Arithmetic Functions and Corresponding Generating Functions. https://doi.org/10.1007/s11785-013-0331-9

I. Cho, Histories Isometries, J. Math (2011) article ID: P110301. 3.

I. Cho (2010) Frames, Fractals and Radial Operators in Hilbert Space. 333-393.

I. Cho (2015) On Dynamical Systems Induced by p-Adic Number Fields.

(2013) Krein-Space Operators Induced by Dirichlet Characters. 3-33.

Ilwoo Cho, Palle Jorgensen (2014) Krein-Space Representations of Arithmetic Functions Determined by Primes. 17(6), 1809-1841. https://doi.org/10.1007/s10468-014-9473-z

T. Gillespie, Functoriality, Univ. of Iowa (2010) Superposition of Zeroes of Automorphic L-Functions and Functoriality.

T. Gillespie, Sci. Math (2011) Prime Number Theorems for Rankin-Selberg L-Functions over Number Fields. 54(1), 35-46.

F. Radulescu (1994) 347 - 389. 347-389.

R. Speicher Combinatorial Theory of the Free Product with Amalgamation and.

Operator-Valued Theory, Amer. Mem (1998) Free Random Variables. 132(627). https://doi.org/10.1090/crmm/001

(1992) Monograph Series. 1.