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arXiv · 1106.2304

E_0-semigroups and q-purity

Christopher Jankowski·Daniel Markiewicz·Robert T. Powers
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Abstract

An E_0-semigroup is called q-pure if it is a CP-flow and its set of flow subordinates is totally ordered by subordination. The range rank of a positive boundary weight map is the dimension of the range of its dual map. Let K be a separable Hilbert space. We describe all q-pure E_0-semigroups of type II_0 which arise from boundary weight maps with range rank one over K. We also prove that no q-pure E_0-semigroups of type II_0 arise from boundary weight maps with range rank two over K. In the case when K is finite-dimensional, we provide a criterion to determine if two boundary weight maps of range rank one over K give rise to cocycle conjugate q-pure E_0-semigroups.

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Christopher Jankowski, Daniel Markiewicz, Robert T. Powers. 2011-06-12. E_0-semigroups and q-purity. https://arxiv.org/abs/1106.2304

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