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arXiv · 1507.01418

A semigroup approach to the numerical range of operators on Banach spaces

Martin Adler·Waed Dada·Agnes Radl
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Abstract

We introduce the numerical spectrum $\sigma_n(A)\subset \mathbb{C}$ of an (unbounded) linear operator $A$ on a Banach space $X$ and study its properties. Our definition is closely related to the numerical range $W(A)$ of $A$ and always yields a superset of $W(A)$. In the case of bounded operators on Hilbert spaces, the two notions coincide. However, unlike the numerical range, $\sigma_n(A)$ is always closed, convex and contains the spectrum of $A$. In the paper we strongly emphasise the connection of our approach to the theory of $C_0$-semigroups.

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BibTeXRIS

Martin Adler, Waed Dada, Agnes Radl. 2015-07-06. A semigroup approach to the numerical range of operators on Banach spaces. https://arxiv.org/abs/1507.01418

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