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Proceedings of the American Mathematical Society

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Exponential nonnegativity

Author: Herbert Weigel
Journal: Proc. Amer. Math. Soc. 132 (2004), 1775-1778
MSC (2000): Primary 45H05
Published electronically: October 15, 2003
MathSciNet review: 2051140
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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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Additional Information

Herbert Weigel
Affiliation: Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Received by editor(s): October 25, 2002
Received by editor(s) in revised form: February 14, 2003
Published electronically: October 15, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society

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