Abstract
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently similar results also hold for suitable families of non-selfadjoint operators in \(\ell ^p ({\mathbb {Z}})\). Here, we generalize this to a large class of bounded linear operator families on Banach-space valued \(\ell ^p\)-spaces over countable discrete groups. We also provide equality of the pseudospectra for operators in such a family. A main tool for our analysis are techniques from limit operator theory.
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Beckus, S., Lenz, D., Lindner, M. et al. On the spectrum of operator families on discrete groups over minimal dynamical systems. Math. Z. 287, 993–1007 (2017). https://doi.org/10.1007/s00209-017-1856-5
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DOI: https://doi.org/10.1007/s00209-017-1856-5