Commutator conditions implying the convergence of the Lie–Trotter products

Kühnemund, Franziska; Wacker, Markus

doi:10.1090/S0002-9939-01-06034-8

Commutator conditions implying the convergence of the Lie–Trotter products
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by Franziska Kühnemund and Markus Wacker PDF

Proc. Amer. Math. Soc. 129 (2001), 3569-3582 Request permission

Abstract:

In this paper we investigate commutator conditions for two strongly continuous semigroups ${(T(t))_{t\geq 0} }$ and ${(S(t))_{t\geq 0} }$ on a Banach space implying the convergence of the Lie–Trotter products $[T(\tfrac {t}{n})S(\tfrac {t}{n})]^n$. The results are then applied to various examples and, in particular, to the Ornstein–Uhlenbeck operator.

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