On the spectrum of positive linear operators with a partition of unity property

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Nagler, Johannes

关键词: Positive linear operator;    Iterates;    Spectrum;    Eigenvalues;   

DOI  :  10.1016/j.jmaa.2014.12.025

来源: Elsevier

【 摘 要 】

We characterize the spectrum of positive linear operators between Banach function spaces having finite rank and a partition of unity property. Our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle. Finally, we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator. (C) 2014 Elsevier Inc. All rights reserved..

【 授权许可】

Free