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The relation of spatial and tensor product of Arveson systems - the random set point of view.
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, DOI: 10.1142/S0219025715500290 (2016)
We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference units, i.e. it is an intrinsic construction. There is a continuous range of examples coming from the zero sets of Bessel processes where the two products do not coincide. The lattice of all subsystems of the tensor product is analysed in different cases. As a by-product, the Arveson systems coming from Bessel zeros prove to be primitive in the sense of Ref. 12.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Continuous Product Systems Of Hilbert Spaces ; Random Sets ; Spatial Product Of Product Systems
ISSN (print) / ISBN
0219-0257
Quellenangaben
Volume: 18,
Issue: 4
Publisher
World Scientific Publishing
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)