E_0-semigroups and q-purity
Operator Algebras
2011-06-14 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1106.2304,
title = {E_0-semigroups and q-purity},
author = {Christopher Jankowski and Daniel Markiewicz and Robert T. Powers},
journal= {arXiv preprint arXiv:1106.2304},
year = {2011}
}
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39 pages