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arXiv · 2601.05025

Spectral Properties of $ C_{0}$-Semigroups of Positive Operators on C$^*$-Algebras

Ulrich Groh
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Abstract

Let $ (T(t))_{t\geq0} $ be a positive $C_{0}$-semigroup with generator $A$ on a C$^*$-algebra or on the predual of a W$^*$-algebra. Then the growth bound $\omega_{0}$ equals $s(A)$. If the spectrum of $A$ is not empty, then $s(A)$, the spectral bound of $A$, is a spectral value.

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Ulrich Groh. 2026-01-08. Spectral Properties of $ C_{0}$-Semigroups of Positive Operators on C$^*$-Algebras. https://arxiv.org/abs/2601.05025

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