Verlagslink DOI: 10.7153/oam-2022-16-40
arXiv ID: 2111.13750v1
Titel: Minimal Families of Limit Operators
Sprache: Englisch
Autor/Autorin: Lindner, Marko  
Schlagwörter: Mathematics - Functional Analysis; Mathematics - Functional Analysis; Mathematics - Spectral Theory; 47B37, Secondary 47A35, 47B36; Limit operators; minimal system; Schrödinger operator; spectrum
Erscheinungs­datum: Jun-2022
Quellenangabe: Operators and Matrices 16 (2) : 529-543 (2022-06)
Zusammenfassung (englisch): 
We study two abstract scenarios, where an operator family has a certain minimality property. In both scenarios, it is shown that norm, spectrum and resolvent are the same for all family members. Both abstract settings are illustrated by practically relevant examples, including discrete Schrödinger operators with periodic, quasiperiodic, almost-periodic, Sturmian and pseudo-ergodic potential. The main tool is the method of limit operators, known from studies of Fredholm operators and convergence of projection methods. We close by connecting this tool to the study of subwords of the operator potential.
URI: http://hdl.handle.net/11420/11125
ISSN: 1846-3886
Zeitschrift: Operators and matrices 
Institut: Mathematik E-10 
Dokumenttyp: Artikel/Aufsatz
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