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- Title
ADELIC ANALYSIS AND FUNCTIONAL ANALYSIS ON THE FINITE ADELE RING.
- Authors
Ilwoo Cho
- Abstract
In this paper, we study operator theory on the *-algebra MP, consisting of all measurable functions on the finite Adele ring Aℚ, in extended free-probabilistic sense. Even though our *-algebra MP is commutative, our Adelic-analytic data and properties on MP are understood as certain free-probabilistic results under enlarged sense of (noncommutative) free probability theory (well-covering commutative cases). From our free-probabilistic model on Aℚ, we construct the suitable Hilbert-space representation, and study a C*-algebra MP generated by MP under representation. In particular, we focus on operator-theoretic properties of certain generating operators on MP.
- Subjects
FREE probability theory; FUNCTIONAL analysis; FINITE rings; C*-algebras; HILBERT space
- Publication
Opuscula Mathematica, 2018, Vol 38, Issue 2, p139
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2018.38.2.139