# Spectrum of Rota-Baxter operators

@article{Gubarev2020SpectrumOR, title={Spectrum of Rota-Baxter operators}, author={Vsevolod Gubarev}, journal={arXiv: Rings and Algebras}, year={2020} }

We prove that the spectrum of every Rota-Baxter operator of weight $\lambda$ on a unital algebraic (not necessarily associative) algebra over a field of characteristic zero is a subset of $\{0,-\lambda\}$. For a finite-dimensional unital algebra the same statement is shown to hold without a restriction on the characteristic of the ground field. Based on these results, we define the Rota-Baxter $\lambda$-index $\mathrm{rb}_\lambda(A)$ of an algebra $A$ as the infimum of the degrees of minimal…

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