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A Non-commutative analogue of Gaussian Hilbert Spaces

Mihai Popa
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Abstract

The paper gives analogues of some starting results in the theory of Gaussian Hilbert Spaces for semicircular distributed random variables. The transition from the commutative to the free frame is done considering matrices of increasing dimension and utilizing the Amitzur-Levitzki Theorem.

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Mihai Popa. 2005-04-22. A Non-commutative analogue of Gaussian Hilbert Spaces. https://arxiv.org/abs/math/0504470

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