Operator-norm approximation of semigroups by quasi-sectorial contractions

Abstract

We extend the Chernoff theory of approximation of contraction semigroups à 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 quasi-sectorial contractions on a Hilbert space in the operator norm. We give necessary and sufficient conditions for the operator-norm convergence of Trotter-type product formulae. © 2001 Academic Press.