Trotter–Kato Product Formula and Operator-Norm Convergence
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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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