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

DOI:
https://doi.org/10.1090/S0002-9939-10-10260-3

Published electronically:
February 25, 2010

MathSciNet review:
2607874

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Abstract | References | Similar Articles | Additional Information

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 -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

Email:
bhat@isibang.ac.in

**Volkmar Liebscher**

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

Email:
volkmar.liebscher@uni-greifswald.de

**Michael Skeide**

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

Email:
skeide@unimol.it

DOI:
https://doi.org/10.1090/S0002-9939-10-10260-3

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.