Note on spectra of non-selfadjoint operators over dynamical systems

Siegfried Beckus; Daniel Lenz; Marko Lindner; Christian Seifert

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arXiv · 1412.5926

Note on spectra of non-selfadjoint operators over dynamical systems

Siegfried Beckus·Daniel Lenz·Marko Lindner·Christian Seifert

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Abstract

We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to pseudo-ergodic elements have the same spectrum and that this spectrum agrees with their essential spectrum. As a consequence we obtain that the spectrum is constant and agrees with the essential spectrum for all elements in the dynamical system if minimality holds.

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BibTeX RIS

Siegfried Beckus, Daniel Lenz, Marko Lindner, Christian Seifert. 2014-12-18. Note on spectra of non-selfadjoint operators over dynamical systems. https://arxiv.org/abs/1412.5926

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