Geodesic
On nonnegative operators and fully cyclic peripheral spectrum
The electronic journal of linear algebra, Tome 3 (1998), pp. 13-22.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The properties of the peripheral spectrum of a nonnegative linear operator $A$ (for which the spectral radius is a pole of its resolvent) in a complex Banach lattice are studied. It is shown, e.g., that the peripheral spectrum of a natural quotient operator is always fully cyclic. We describe when the nonnegative eigenvectors corresponding to the spectral radius $r$ span the kernel $N(r- A)$. Finally, we apply our results to the case of a nonnegative matrix, and show that they sharpen earlier results by B.-S. Tam [Tamkang J. Math. 21, No. 1, 65-70 (1990; Zbl 0711.15017)] on such matrices and full cyclicity of the peripheral spectrum.
Classification : 47B65, 47A10, 15A48 
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     title = {On nonnegative operators and fully cyclic peripheral spectrum},
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Förster, K.-H.; Nagy, B. On nonnegative operators and fully cyclic peripheral spectrum. The electronic journal of linear algebra, Tome 3 (1998), pp. 13-22. http://geodesic.mathdoc.fr/item/ELA_1998__3__a9/