Abstract
For families of magnetic self-adjoint operators on \(\mathbb Z^d\) whose symbols and magnetic fields depend continuously on a parameter \(\epsilon \), it is shown that the spectrum of these operators also varies continuously with respect to \(\epsilon \). The proof is based on an algebraic setting involving twisted crossed product \(C^*\)-algebras.
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S. Richard is on leave of absence from Université de Lyon; Université Lyon 1; CNRS, UMR5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France.
The work of S. Richard is supported by JSPS Grant-in-Aid for Young Scientists (A) No. 26707005.
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Parra, D., Richard, S. Continuity of the spectra for families of magnetic operators on \(\mathbb Z^d\) . Anal.Math.Phys. 6, 327–343 (2016). https://doi.org/10.1007/s13324-015-0121-5
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DOI: https://doi.org/10.1007/s13324-015-0121-5