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arXiv · 1703.09536

Remarks on the operator-norm convergence of the Trotter product formula

Hagen Neidhardt·Artur Stephan·Valentin A. Zagrebnov
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Abstract

We revise the operator-norm convergence of the Trotter product formula for a pair {A,B} of generators of semigroups on a Banach space. Operator-norm convergence holds true if the dominating operator A generates a holomorphic contraction semigroup and B is a A-infinitesimally small generator of a contraction semigroup, in particular, if B is a bounded operator. Inspired by studies of evolution semigroups it is shown in the present paper that the operator-norm convergence generally fails even for bounded operators B if A is not a holomorphic generator. Moreover, it is shown that operator norm convergence of the Trotter product formula can be arbitrary slow.

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Hagen Neidhardt, Artur Stephan, Valentin A. Zagrebnov. 2017-03-28. Remarks on the operator-norm convergence of the Trotter product formula. https://arxiv.org/abs/1703.09536

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