Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Exponential nonnegativity

Author(s): Herbert Weigel
Journal: Proc. Amer. Math. Soc. 132 (2004), 1775-1778.
MSC (2000): Primary 45H05
Posted: October 15, 2003
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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 $C$.

References:

[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

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 45H05

Retrieve articles in all Journals with MSC (2000): 45H05

Additional Information:

Herbert Weigel
Affiliation: Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: herbert.weigel@math.uni-karlsruhe.de

DOI: 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
Posted: October 15, 2003
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google