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Exponential nonnegativity


Author: Herbert Weigel
Journal: Proc. Amer. Math. Soc. 132 (2004), 1775-1778
MSC (2000): Primary 45H05
DOI: https://doi.org/10.1090/S0002-9939-03-07297-6
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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  • [1] A. Berman, M. Neumann and R. J. Stern, Nonnegative matrices in dynamic systems, Pure and Applied Mathematics, John Wiley and Sons, New York, 1989. MR 90j:93030
  • [2] A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, 1979. MR 82b:15013
  • [3] L. Elsner, Monotonie und Randspektrum bei vollstetigen Operatoren, Arch. Rational Mech. Anal. 36 (1970), 356-365. MR 40:4804
  • [4] G. Herzog and R. Lemmert, On quasipositive elements in ordered Banach algebras, Studia Math. 129 (1998), 59-65. MR 99g:46061
  • [5] G. Herzog and Ch. Schmoeger, A note on a Theorem of Raubenheimer and Rode, Proc. Amer. Math. Soc. 131 (2003), 3507-3509.
  • [6] H. Raubenheimer and S. Rode, Cones in Banach algebras, Indag. Math. 7 (1996), 489-502. MR 99i:46035
  • [7] C. Schmoeger, Remarks on commuting exponentials in Banach algebras, Proc. Amer. Math. Soc. 127 (1999), 1337-1338. MR 99h:46090
  • [8] J. S. Vandergraft, Spectral properties of matrices which have invariant cones, SIAM J. Appl. Math. 16 (1968), 1208-1222.MR 39:5599

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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: https://doi.org/10.1090/S0002-9939-03-07297-6
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

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