The Spatial Product of Arveson Systems is Intrinsic
B.V. Rajarama Bhat, Volkmar Liebscher, Mithun Mukherjee, Michael, Skeide
TL;DR
This paper proves that the spatial product of two spatial Arveson systems is intrinsic and does not depend on the choice of reference units, also extending this to minimal dilations of Powers sums of spatial CP-semigroups.
Contribution
It establishes the independence of the spatial product of Arveson systems from reference units and applies this to minimal dilations of CP-semigroups.
Findings
Spatial product is independent of reference units.
Minimal dilation of Powers sum is unique up to cocycle conjugacy.
Answers an open question in the theory of Arveson systems.
Abstract
We prove that the spatial product of two spatial Arveson systems is independent of the choice of the reference units. This also answers the same question for the minimal dilation the Powers sum of two spatial CP-semigroups: It is independent up to cocycle conjugacy.
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