Neidhardt H., Zagrebnov V.A.
Trotter-Kato product formula and operator-norm convergence
(75K, LATeX)

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.