On the spectrum of positive finite-rank operators with a partition of unity property

2014/03/18 by Johannes Nagler, Nagler, Johannes
Engineering · Mathematics · #41A36 #47A05 #47A10 #Advanced Numerical Analysis Techniques #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1403.4522

openalex publication_date 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the spectrum of positive linear operators T:X → Y, where X and Y are complex Banach function spaces with unit 1, having finite rank and a partition of unity property. Then all the points in the spectrum are eigenvalues of T and σ_p(T) ⊂ B(0,1) ∪ \1\. The main result is that 1 is the only eigenvalue on the unit circle, the peripheral spectrum of T.

Citations

• Lower bounds for the approximation with variation-diminishing splines

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