Matrices induced by arithmetic functions acting on certain Krein spaces. (English) Zbl 1380.05197
Summary: In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
MSC:
05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
11G15 | Complex multiplication and moduli of abelian varieties |
11R04 | Algebraic numbers; rings of algebraic integers |
11R09 | Polynomials (irreducibility, etc.) |
11R47 | Other analytic theory |
11R56 | Adèle rings and groups |
46L10 | General theory of von Neumann algebras |
46L40 | Automorphisms of selfadjoint operator algebras |
46L53 | Noncommutative probability and statistics |
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 |
Keywords:
primes; arithmetic functions; the arithmetic algebra; linear functionals; arithmetic probability spaces; Krein spaces; Krein-space operatorsReferences:
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