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

Johannes Nagler

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arXiv · 1403.4522

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

Johannes Nagler

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Abstract

We characterize the spectrum of positive linear operators $T:X \to Y$, 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 $σ_p(T) \subset B(0,1) \cup \{1\}$. The main result is that $1$ is the only eigenvalue on the unit circle, the peripheral spectrum of $T$.

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Johannes Nagler. 2014-03-18. On the spectrum of positive finite-rank operators with a partition of unity property. https://arxiv.org/abs/1403.4522

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