Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Jankowski, Christopher, Markiewicz, Daniel, Powers, Robert T.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1504112190