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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)
Postprint DOI
Open Access Green
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Continuous Product Systems Of Hilbert Spaces ; Random Sets ; Spatial Product Of Product Systems
ISSN (print) / ISBN 0219-0257
Quellenangaben Band: 18, Heft: 4 Seiten: , Artikelnummer: , Supplement: ,
Verlag World Scientific Publishing
Begutachtungsstatus Peer reviewed