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arXiv · 1612.09414

From discrete to continuous monotone $C^*$-algebras via quantum central limit theorems

Vitonofrio Crismale·Francesco Fidaleo·Yun Gang Lu
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Abstract

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 operators on a $C^*$-algebra, at least when the test functions are Riemann integrable. Namely, the approximation is given by weighted sequences of creators and annihilators in discrete monotone $C^*$-algebras, the weight being the above cited test functions. The construction is then generalized to processes by an invariance principle.

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Vitonofrio Crismale, Francesco Fidaleo, Yun Gang Lu. 2016-12-30. From discrete to continuous monotone $C^*$-algebras via quantum central limit theorems. https://arxiv.org/abs/1612.09414

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