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Minimal Families of Limit Operators
Publikationstyp
Journal Article
Publikationsdatum
2022-06
Sprache
English
Author
Institut
Enthalten in
Volume
16
Issue
2
Start Page
529
End Page
543
Citation
Operators and Matrices 16 (2): 529-543 (2022-06)
Publisher DOI
Scopus ID
ArXiv ID
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.
Schlagworte
Mathematics - Functional Analysis
Mathematics - Functional Analysis
Mathematics - Spectral Theory
47B37, Secondary 47A35, 47B36
Limit operators
minimal system
Schrödinger operator
spectrum
DDC Class
000: Allgemeines, Wissenschaft
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