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Positive operator-valued kernels and non-commutative probability
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Positive operator-valued kernels and non-commutative probability

Palle E. T Jorgensen and James Tian
arXiv.org
Cornell University
05/15/2024
DOI: 10.48550/arxiv.2405.09315
url
https://doi.org/10.48550/arxiv.2405.09315View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We prove new factorization and dilation results for general positive operator-valued kernels, and we present their implications for associated Hilbert space-valued Gaussian processes, and their covariance structure. Further applications are to non-commutative probability theory, including a non-commutative Radon--Nikodym theorem for systems of completely positive maps.
Mathematics - Functional Analysis Mathematics - Mathematical Physics Mathematics - Operator Algebras Physics - Mathematical Physics Physics - Quantum Physics

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