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arXiv · 0810.3072

Numerical Range and Quasi-Sectorial Contractions

Yury Arlinskii·Valentin Zagrebnov
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Abstract

We apply a method developed by one of the authors, see \cite{Arl1}, to localize the numerical range of \textit{quasi-sectorial} contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups $\{\exp(- t S)\}_{t\ge 0}$, 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: $\exp(- t S)=\lim\limits_{n\to \infty}(I+tS/n)^{-n}$, $t\ge 0$, for this class of semigroups.

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Yury Arlinskii, Valentin Zagrebnov. 2008-10-17. Numerical Range and Quasi-Sectorial Contractions. https://arxiv.org/abs/0810.3072

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