Numerical Range and Quasi-Sectorial Contractions

2008/10/17 by Arlinskii, Yury, Zagrebnov, Valentin · 1 citation
#47A55 #47D03 #81Q10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0810.3072

Abstract

We apply a method developed by one of the authors, see \citeArl1, to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups \exp(- t S)\_{t≥ 0}, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation: exp(- t S)=lim_{n→ ∞}(I+tS/n)^-n, t≥ 0, for this class of semigroups.

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• An introduction of Berezin sectorial operators and its application to Berezin number inequalities

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