ELA, Volume 3, pp. 13-22, February 1998, abstract.

On nonnegative operators and fully cyclic peripheral spectrum

K.-H. Foerster and B. Nagy


In this note 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. 21:65-70, 1990] on such matrices and full 
cyclicity of the peripheral spectrum.