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

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 ).

Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Qp over Primes p

In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS .