5 papers
Freedman's theorem for unitarily invariant states on the CCR algebra
Vitonofrio Crismale, Simone Del Vecchio, Tommaso Monni +1
The set of states on , the CCR algebra of a separable Hilbert space , is here looked at as a natural object to obtain a non-commutative version of Freedman's t…
On truncated -free Fock spaces: spectrum of position operators and shift-invariant states
Vitonofrio Crismale, Simone Del Vecchio, Stefano Rossi
The ergodic properties of the shift on both full and -truncated -free -algebras are analyzed. In particular, the shift is shown to be uniquely ergodic with respect to th…
Tail algebras for monotone and -deformed exchangeable stochastic processes
Vitonofrio Crismale, Stefano Rossi
We compute the tail algebras of exchangeable monotone stochastic processes. This allows us to prove the analogue of de Finetti's theorem for this type of processes. In addition, si…
On -norms on -graded tensor products
Vitonofrio Crismale, Stefano Rossi, Paola Zurlo
We systematically investigate -norms on the algebraic graded product of -graded -algebras. This requires to single out the notion of a compatible norm, that…
From discrete to continuous monotone -algebras via quantum central limit theorems
Vitonofrio Crismale, Francesco Fidaleo, Yun Gang Lu
We prove that all finite joint distributions of creation and annihilation operators in Monotone and anti-Monotone Fock spaces can be realized as Quantum Central Limit of certain op…