Bures distance and transition probability for $\alpha$-CPD-kernels

Santanu Dey; Harsh Trivedi

doi:10.1007/s11785-018-0798-1

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arXiv · 1605.04529

Bures distance and transition probability for $\alpha$-CPD-kernels

Santanu Dey·Harsh Trivedi

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Abstract

If the symmetry (fixed invertible self adjoint map) of Krein spaces is replaced by a fixed unitary, then we obtain the notion of S-spaces which was introduced by Szafraniec. Assume $\alpha$ to be an automorphism on a $C^*$-algebra. In this article, we obtain the Kolmogorov decomposition of $\alpha$-completely positive definite (or $\alpha$-CPD-kernels for short) and investigate the Bures distance between $\alpha$-CPD-kernels. We also define transition probability for these kernels and find a characterization of the transition probability.

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BibTeX RIS

Santanu Dey, Harsh Trivedi. 2016-05-15. Bures distance and transition probability for $\alpha$-CPD-kernels. https://doi.org/10.1007/s11785-018-0798-1

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