On the spectrum of operator families on discrete groups over minimal dynamical systems

2016/06/27 by Beckus, Siegfried, Lenz, Daniel, Lindner, Marko +1
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1606.08353

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 ℓ^p (\ZM). Here, we generalize this to a large class of bounded linear operator families on Banach-space valued ℓ^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.

Related

• Note on spectra of non-selfadjoint operators over dynamical systems
• Spectrum of a family of operators
• Local spectrum of a family of operators
• Minimal Families of Limit Operators
• Minimal Families of Limit Operators