Annals of Functional Analysis

Actions of arithmetic functions on matrices and corresponding representations

Ilwoo Cho and Palle Jorgensen

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Abstract

In this paper, we study a class of representations of arithmetic functions, and corresponding operator-theoretic and free probabilistic properties. We associate given arithmetic functions $f$ to certain matrices $\alpha _{n}(f).$

Article information

Source
Ann. Funct. Anal., Volume 5, Number 2 (2014), 90-117.

Dates
First available in Project Euclid: 7 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1396833506

Digital Object Identifier
doi:10.15352/afa/1396833506

Mathematical Reviews number (MathSciNet)
MR3192013

Zentralblatt MATH identifier
1309.46037

Subjects
Primary: 46L53: Noncommutative probability and statistics
Secondary: 46L54: Free probability and free operator algebras 47L15: Operator algebras with symbol structure 47L30: Abstract operator algebras on Hilbert spaces 47L55: Representations of (nonselfadjoint) operator algebras 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 11R04: Algebraic numbers; rings of algebraic integers 11R09: Polynomials (irreducibility, etc.) 11R47: Other analytic theory [See also 11Nxx] 11R56: Adèle rings and groups 46L10: General theory of von Neumann algebras 46L40: Automorphisms

Keywords
Arithmetic function arithmetic algebra linear functional arithmetic prime probability space Krein space representation convolution operator multiplication operator

Citation

Cho, Ilwoo; Jorgensen, Palle. Actions of arithmetic functions on matrices and corresponding representations. Ann. Funct. Anal. 5 (2014), no. 2, 90--117. doi:10.15352/afa/1396833506. https://projecteuclid.org/euclid.afa/1396833506


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