00-277 Cachia V. , Zagrebnov V. A.
OPERATOR-NORM APPROXIMATION OF SEMIGROUPS BY SECTORIAL CONTRACTIONS (71K, LATeX 2.09) Jun 20, 00
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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.

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