We exhibit a Hamel basis for the concrete *-algebra ${gam_o}$ associated to monotone commutation relations realised on the monotone Fock space, mainly composed by Wick ordered words of annihilators and creators. We apply such a result to investigate spreadability and exchangeability of the stochastic processes arising from such commutation relations. In particular, we show that spreadability comes from a monoidal action implementing a dissipative dynamics on the norm closure C*-algebra $gam=overline{gam_o}$. Moreover, we determine the structure of spreadable and exchangeable monotone stochastic processes using their correspondence with spreading invariant and symmetric monotone states, respectively.
Wick order, spreadability and exchangeability for monotone commutation relations
Vitonofrio Crismale;Maria Elena Griseta
2018-01-01
Abstract
We exhibit a Hamel basis for the concrete *-algebra ${gam_o}$ associated to monotone commutation relations realised on the monotone Fock space, mainly composed by Wick ordered words of annihilators and creators. We apply such a result to investigate spreadability and exchangeability of the stochastic processes arising from such commutation relations. In particular, we show that spreadability comes from a monoidal action implementing a dissipative dynamics on the norm closure C*-algebra $gam=overline{gam_o}$. Moreover, we determine the structure of spreadable and exchangeable monotone stochastic processes using their correspondence with spreading invariant and symmetric monotone states, respectively.File | Dimensione | Formato | |
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