Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Author: Skeide, Michael
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211717
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations. Michael Skeide. SIGMA 18 (2022), 071, 8 pages

We present, for the first time, the result (from 2008) that (normal, strongly continuous) Markov semigroups on () ( a separable Hilbert space) admit a Hudson-Parthasarathy dilation (that is, a dilation to a cocycle perturbation of a noise) if and only if the Markov semigroup is spatial (that is, if...