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Communications in Mathematical Physics

, Volume 205, Issue 1, pp 129–159 | Cite as

Trotter–Kato Product Formula and Operator-Norm Convergence

  • H. Neidhardt
  • V. A. Zagrebnov
Article

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • H. Neidhardt
    • 1
  • V. A. Zagrebnov
    • 2
  1. 1.Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany Germany
  2. 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.frFrance

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