# Continuity of the spectra for families of magnetic operators on $$\mathbb Z^d$$ Z d

Continuity of the spectra for families of magnetic operators on $$\mathbb Z^d$$ Z d For families of magnetic self-adjoint operators on $$\mathbb Z^d$$ Z d whose symbols and magnetic fields depend continuously on a parameter $$\epsilon$$ ϵ , it is shown that the spectrum of these operators also varies continuously with respect to $$\epsilon$$ ϵ . The proof is based on an algebraic setting involving twisted crossed product $$C^*$$ C ∗ -algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Continuity of the spectra for families of magnetic operators on $$\mathbb Z^d$$ Z d

, Volume 6 (4) – Jan 13, 2016
17 pages

/lp/springer-journals/continuity-of-the-spectra-for-families-of-magnetic-operators-on-mathbb-eK2gMo16uL
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-015-0121-5
Publisher site
See Article on Publisher Site

### Abstract

For families of magnetic self-adjoint operators on $$\mathbb Z^d$$ Z d whose symbols and magnetic fields depend continuously on a parameter $$\epsilon$$ ϵ , it is shown that the spectrum of these operators also varies continuously with respect to $$\epsilon$$ ϵ . The proof is based on an algebraic setting involving twisted crossed product $$C^*$$ C ∗ -algebras.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jan 13, 2016