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Subsystems of Fock need not be Fock: Spatial CP-semigroups

Authors: B. V. Rajarama Bhat, Volkmar Liebscher and Michael Skeide
Journal: Proc. Amer. Math. Soc. 138 (2010), 2443-2456
MSC (2010): Primary 46L53, 46L55, 60J25
Published electronically: February 25, 2010
MathSciNet review: 2607874
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Abstract: We show that a product subsystem of a time ordered system (that is, a product system of time ordered Fock modules), even one of type I, need not be isomorphic to a time ordered product system. In this way, we answer an open problem in the classification of CP-semigroups by product systems. We define spatial strongly continuous CP-semigroups on a unital $ C^*$-algebra and characterize them as those CP-semigroups that have a Christensen-Evans generator.

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Additional Information

B. V. Rajarama Bhat
Affiliation: Statistics and Mathematics Unit, Indian Statistical Institute Bangalore, R. V. College Post, Bangalore 560059, India

Volkmar Liebscher
Affiliation: Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, 17487 Greifswald, Germany

Michael Skeide
Affiliation: Dipartimento S.E.G.e S., Universita degli Studi del Molise, Via de Sanctis, 86100 Campobasso, Italy

Received by editor(s): April 14, 2008
Received by editor(s) in revised form: July 31, 2009, and September 23, 2009
Published electronically: February 25, 2010
Additional Notes: This work was supported by an RiP-Program at Mathematisches Forschungsinstitut Oberwolfach. The first author is supported by the Department of Science and Technology, India, under the Swarnajayanthi Fellowship Project. The third author was supported by research funds from the Dipartimento S.E.G.e S. of the University of Molise and from the Italian MUR (PRIN 2005 and 2007).
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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