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TROTTER PRODUCT FORMULA FOR NONSELF-ADJOINT GIBBS SEMIGROUPS

Published online by Cambridge University Press:  30 October 2001

VINCENT CACHIA  and
VALENTIN A. ZAGREBNOV
VINCENT CACHIA
Affiliation:
Centre de Physique Théorique, CNRS Luminy, Case 907 F-13288 Marseille, Cedex 9, France; cachia@cpt.univ-mrs.fr, zagrebnov@cpt.univ-mrs.fr
VALENTIN A. ZAGREBNOV
Affiliation:
Centre de Physique Théorique, CNRS Luminy, Case 907 F-13288 Marseille, Cedex 9, France; cachia@cpt.univ-mrs.fr, zagrebnov@cpt.univ-mrs.fr
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Abstract

The trace-norm convergence of the Trotter product formula is proved for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e−tReA is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 436 - 444
Copyright
The London Mathematical Society 2001

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