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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: herbert.weigel@math.uni-karlsruhe.de

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07297-6
PII: S 0002-9939(03)07297-6
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