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Operator-Norm Approximation of Semigroups by Quasi-sectorial Contractions

✍ Scribed by Vincent Cachia; Valentin A. Zagrebnov

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 223 KB
Volume: 180
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3693

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✦ Synopsis

We extend the Chernoff theory of approximation of contraction semigroups aÁ 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.

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This paper is devoted to the study of contraction semigroups generated by linear partial differential operators. It is shown that linear partial differential operators of order higher than two cannot generate contraction semigroups on (L p ) N for p # [1, ) unless p=2. If p>1 and the L p -dissipativ