Positive operator-valued kernels and non-commutative probability

• URL: http://arxiv.org/abs/2405.09315v1
• Date: Wed, 15 May 2024 13:16:11 GMT
• Title: Positive operator-valued kernels and non-commutative probability
• Authors: Palle E. T. Jorgensen, James Tian,
• Abstract summary: We prove new factorization and dilation results for general positive operator-valued kernels. We present their implications for associated Hilbert space-valued Gaussian processes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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