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Article Dans Une Revue Integral Equations and Operator Theory Année : 2018

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

Résumé

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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Dates et versions

hal-01497909 , version 1 (29-03-2017)

Identifiants

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Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov. Remarks on the operator-norm convergence of the Trotter product formula. Integral Equations and Operator Theory, 2018, 90 (2), pp.UNSP 15. ⟨10.1007/s00020-018-2424-z⟩. ⟨hal-01497909⟩
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