Cachia V. , Zagrebnov V. A.
OPERATOR-NORM APPROXIMATION OF SEMIGROUPS BY SECTORIAL CONTRACTIONS
(71K, LATeX 2.09)
ABSTRACT. We extend the Chernoff theory for approximation of contraction semigroups \`a
la Trotter. We show that the Trotter-Neveu-Kato convergence theorem holds in
operator norm for a family of uniformly m-sectorial generators in a Hilbert
space. Then we obtain a Chernoff-type approximation theorem for sectorial
contractions on a Hilbert space in the operator norm. As examples we give
necessary and sufficient conditions for the operator-norm convergence of
Trotter-type product formulae.