Publisher DOI: 10.1007/s00209-017-1856-5
Title: On the spectrum of operator families on discrete groups over minimal dynamical systems
Language: English
Authors: Beckus, Siegfried 
Lenz, Daniel 
Lindner, Marko  
Seifert, Christian  
Keywords: Minimal dynamical system; P-Theory; Pseudo-ergodicity; Spectrum
Issue Date: 1-Dec-2017
Source: Mathematische Zeitschrift 3-4 (287): 993-1007 (2017-12-01)
Abstract (english): 
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 ℓp(Z). Here, we generalize this to a large class of bounded linear operator families on Banach-space valued ℓp-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.
URI: http://hdl.handle.net/11420/3772
ISSN: 0025-5874
Journal: Mathematische Zeitschrift 
Institute: Mathematik E-10 
Document Type: Article
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