Exponential nonnegativity

Weigel, Herbert

doi:10.1090/S0002-9939-03-07297-6

Exponential nonnegativity
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by Herbert Weigel PDF

Proc. Amer. Math. Soc. 132 (2004), 1775-1778 Request permission

Abstract:

Let $A$ be a Banach algebra, $a\in A$, $\sigma (a)$ the spectrum of $a$ and $\tau (a)$ the spectral abscissa of $a$. If $\tau (a) \in \sigma (a)$, then we show that there exists an algebra cone $C \subseteq A$ such that $a$ is exponentially nonnegative with respect to $C$ and the spectral radius is increasing on $C$.

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