A semigroup Approach to Numerical Ranges of Operators on Banach Spaces.

Beschreibung

We develop a semigroup approach to the "numerical spectrum", a modification of the usual numerical range of a linear operator on a Banach space eliminating some of its deficits. Our definition is based on the Hille-Yosida and Lumer-Phillips theorems and yields a series of different characterizations. In particular, our numerical spectrum is always closed and convex and contains the spectrum of the operator. We determine the numerical spectrum in many concrete cases and investigate its behavior under perturbation and under positivity assumptions.

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