2022
DOI: 10.48550/arxiv.2202.01298
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Free noncommutative hereditary kernels: Jordan decomposition, Arveson extension, kernel domination

Abstract: We discuss a (i) quantized version of the Jordan decomposition theorem for a complex Borel measure on a compact Hausdorff space, namely, the more general problem of decomposing a general noncommutative kernel (a quantization of the standard notion of kernel function) as a linear combination of completely positive noncommutative kernels (a quantization of the standard notion of positive definite kernel). Other special cases of (i) include: the problem of decomposing a general operator-valued kernel function as … Show more

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