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- W4287640223 abstract "We consider contractive operators $T$ that are trace class perturbations of a unitary operator $U$. We prove that the dimension functions of the absolutely continuous spectrum of $T$, $T^*$ and of $U$ coincide. In particular, if $U$ has a purely singular spectrum then the characteristic function $theta$ of $T$ is a two-sided inner function, i.e. $theta(xi)$ is unitary a.e. on $mathbb{T}$. Some corollaries of this result are related to investigations of the asymptotic stability of the operators $T$ and $T^*$ (convergence $T^nto 0$ and $(T^*)^nto 0$, respectively, in the strong operator topology). The proof is based on an explicit computation of the characteristic function." @default.
- W4287640223 created "2022-07-25" @default.
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- W4287640223 date "2020-10-15" @default.
- W4287640223 modified "2023-09-25" @default.
- W4287640223 title "Preservation of absolutely continuous spectrum for contractive operators" @default.
- W4287640223 doi "https://doi.org/10.48550/arxiv.2010.07908" @default.
- W4287640223 hasPublicationYear "2020" @default.
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