Banach *-algebras generated by semicircular elements induced by certain orthogonal projections

• Autorzy: Cho I. , Jorgensen P. E. T.

Identyfikatory

DOI

10.7494/OpMath.2018.38.4.501

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

free probability; orthogonal projections; weighted-semicircular elements; semicircular elements

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 4
• Strony: 501--535
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Cho I.

• Saint Ambrose University Department of Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA

autor

Jorgensen P. E. T.

• The University of Iowa Department of Mathematics Iowa City, IA 52242-1419, USA

Bibliografia

• [1] M. Brannan, K. Kirkpatrick, Quantum groups and generalized circular elements, Pacific J. Math. 282 (2016) 1, 35-61.
• [2] I. Cho, On dynamical systems induced by p-adic number fields, Opuscula Math. 35 (2015) 4, 445-484.
• [3] I. Cho, p-adic free stochastic integrals for p-adic weighted-semi circular motions determined by primes p, Libertas Math. (New Series) 36 (2016) 2, 65-110.
• [4] I. Cho, Free semicircular families in free product Banach ^-algebras induced by p-adic number fields, Complex Anal. Oper. Theory 11 (2017) 3, 507-565.
• [5] I. Cho, P.E.T. Jorgensen, Semicircular elements induced by p-adic number fields, Opuscula Math. 37 (2017) 5, 665-703.
• [6] A. Deya, R. Schott, On the rough-paths approach to noncommutative stochastic calculus, J. Funct. Anal. 265 (2013) 4, 594-628.
• [7] T. Gillespie, Prime number theorems for Rankin-Selberg L-functions over number fields, Sci. China Math. 54 (2011) 1, 35-46.
• [8] I. Gomez, M. Caetagnino, A quantum, version of spectral decomposition theorem, of dynamical systems, Quantum Chaos Hierarchy: Ergodic, Mixing and Exact, Chaos Solitons Fractals 70 (2015), 99-116.
• [9] N.A. Ivanov, T. Omland, C* -simplicity of free products with amalgamation and radical classes of groups, J. Funct. Anal. 272 (2017) 9, 3712-3741.
• [10] Y. Liu, Y. Yu, On an extension of Stevic-Sharma operator from the general space to weighted-type spaces on the unit ball, Complex Anal. Oper. Theory 11 (2017) 2, 261-288.
• [11] M.A. Navarro, S. Villegas, Semi-stable radial solutions of p-Laplace equations in M,N, Nonlinear Anal. 149 (2017), 111-116.
• [12] A. Nica, Free probability aspect of irreducible meandric systems, and some related observations about meanders, Infinite Dimes. Anal. Quantum Probab. Relat. Top. 19 (2016) 2, 1650011, 22 pp.
• [13] F. Radulescu, Random, matrices, amalgamated free products and subfactors of the C*-algebra of a free group of nonsingular index, Invent. Math. 115 (1994), 347-389.
• [14] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Amer. Math. Soc. Mem. 132 (1998) 627.
• [15] V.S. Vladimirov, LV. Volovich, E.I. Zelenov, p-adic analysis and mathematical physics, Ser. Soviet & East European Math., vol. 1, World Scientific, 1994.
• [16] D. Voiculescu, K. Dykemma, A. Nica, Free random variables, CRM Monograph Series, vol. 1, Amer. Math. Soc, Providence, 1992.
• [17] Y. Yin, Z. Bai, J. Hu, On the semicircular law of larg e-dimensional random quaternion matrices, J. Theor. Probab. 29 (2016) 3, 1100-1120.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).