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Commutator conditions implying the convergence of the Lie-Trotter products |
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| Authors: | Franziska Kü hnemund Markus Wacker |
| Institution: | Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany ; Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany |
| Abstract: | In this paper we investigate commutator conditions for two strongly continuous semigroups |
| Keywords: | Strongly continuous semigroups Trotter--Lie product formula commutator conditions Weyl relation Ornstein--Uhlenbeck semigroup |
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and 
on a Banach space implying the convergence of the Lie-Trotter products ![$T(\tfrac{t}{n})S(\tfrac{t}{n})]^n$](http://www.ams.org/proc/2001-129-12/S0002-9939-01-06034-8/gif-abstract0/img3.gif){kind=small}
. The results are then applied to various examples and, in particular, to the Ornstein-Uhlenbeck operator.