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Trotter–Kato Product Formula and Operator-Norm Convergence

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Abstract:

We find necessary and sufficient conditions for the operator-norm convergence of the Trotter–Kato product formula. Using them we prove that this convergence takes place: (i) if the resolvent of one of the involved operators is compact, either (ii) if one operator is relatively compact with respect to another one, or (iii) if the product of resolvents of the involved operators is compact.

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Authors and Affiliations

  1. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany , Germany

    H. Neidhardt

  2. Départment de Physique, Université de la Méditerranée (Aix-Marseille II), and CPT-Luminy, Case 907, 13288 Marseille Cedex 9, France. E-mail: zagrebnov@cpt.univ-mrs.fr, France

    V. A. Zagrebnov

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  1. H. Neidhardt
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  2. V. A. Zagrebnov
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Received: 19 October 1998 / Accepted: 22 February 1999

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Neidhardt, H., Zagrebnov, V. Trotter–Kato Product Formula and Operator-Norm Convergence. Commun. Math. Phys. 205, 129–159 (1999). https://doi.org/10.1007/s002200050671

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  • DOI: https://doi.org/10.1007/s002200050671

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