Banach-Space Operators Acting on Semicircular Elements Induced by p -Adic Number Fields over Primes p

Ilwoo Cho
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Ilwoo Cho: Department of Mathematics and Statistics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA

Mathematics, 2019, vol. 7, issue 6, 1-44

Abstract: In this paper, we study certain Banach-space operators acting on the Banach *-probability space ( LS , τ 0 ) generated by semicircular elements Θ p , j induced by p -adic number fields Q p over the set P of all primes p . Our main results characterize the operator-theoretic properties of such operators, and then study how ( LS , τ 0 ).

Keywords: free probability; p-adic number fields; weighted-semicircular elements; semicircular elements; the semicircular adelic filterization; shifts on P×Z; free homomorphisms; prime-integer-shift operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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