On the continuity of spectra for families of magnetic pseudodifferential operators

Journal of Mathematical Physics

Volumn 51, Issue 8, 2010, Pages

  Athmouni, Nassim ^a   Mǎntoiu, Marius ^b   Purice, Radu ^c  

^a UNIVERSITY OF SFAX   (Tunisia)

^b UNIVERSITY OF CHILE   (Chile)

^c INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78049439714     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3470118     Document Type: Article

References (25)

1. Amrein W.O. Boutet de Monvel A. Georgescu V. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians 1996, and (Birkhäuser, Basel, ).
2. Avron J. Simon B. Stability of gaps for periodic potentials under a variation of the magnetic field. J. Phys. A 1985, 18:2199. JPHAC5, 0305-4470, 10.1088/0305-4470/18/12/017.
3. Bellissard J. Lipschitz continuity of gap boundaries for Hofstadter-like spectra. Commun. Math. Phys. 1994, 160:599. CMPHAY, 0010-3616, 10.1007/BF02173432.
4. Bellissard J. Iochum B. Testard D. Continuity properties of the electronic spectrum of 1D quasicrystals. Commun. Math. Phys. 1991, 141:353. CMPHAY, 0010-3616, 10.1007/BF02101510.
5. *-algèbres de Hopf. Bull. Soc. Math. France 1996, 124:141. BSMFAA, 0037-9484.
6. Briet P. Cornean H.D. Locating the spectrum for magnetic Schrödinger and Dirac operators. Commun. Partial Differ. Equ. 2002, 27:1079. CPDIDZ, 0360-5302, 10.1081/PDE-120004894.
7. Dixmier J. Les C*-algèbres et leurs représentations 1964, (Gauthier-Villars, Paris)
8. Elliott G. Gaps in the spectrum of an almost periodic Schrödinger operator. C. R. Math. Rep. Acad. Sci. Canada 1982, 4:255. 0706-1994.
9. Fell J.M. G. The structure of algebras of operator fields. Acta Math. 1961, 106:233. ACMAA8, 0001-5962, 10.1007/BF02545788.
10. *-algebras and spectral analysis of quantum Hamiltonians. Commun. Math. Phys. 2002, 228:519. CMPHAY, 0010-3616, 10.1007/s002200200669.
11. Iftimie V. Opérateurs differentiels magnétiques: Stabilité des trous dans le spectre, invariance du spectre essentiel et applications. Commun. Partial Differ. Equ. 1993, 18:651. CPDIDZ, 0360-5302, 10.1080/03605309308820944.
12. Iftimie V. Mǎntoiu M. Purice R. Magnetic pseudodifferential operators. Publ. Res. Inst. Math. Sci. 2007, 43:585. KRMPBV, 0034-5318, 10.2977/prims/1201012035.
13. Karasev M.V. Osborn T.A. Symplectic areas, quantization and dynamics in electromagnetic fields. J. Math. Phys. 2002, 43:756. JMAPAQ, 0022-2488, 10.1063/1.1426688.
14. *-algebras. Publ. Res. Inst. Math. Sci. KRMPBV, 0034-5318, and (to be published).
15. Mǎntoiu M. Purice R. The magnetic Weyl calculus. J. Math. Phys. 2004, 45:1394. JMAPAQ, 0022-2488, 10.1063/1.1668334.
16. Mǎntoiu M. Purice R. Mathematical Physics of Quantum Mechanics 2006, 690:417-434. 10.1007/3-540-34273-7_30, and Lecture Notes in Physics Vol. (Springer, Berlin, ), pp.
17. Mǎntoiu M. Purice R. Richard S. Advances in Operator Algebras and Mathematical Physics 2005, 137-172. and Twisted crossed products and magnetic pseudodifferential operators, in pp. Theta Ser. Adv. Math., 5, Theta, Bucharest.
18. *-algebraic approach. J. Funct. Anal. 2007, 250:42. JFUAAW, 0022-1236, 10.1016/j.jfa.2007.05.020.
19. Nenciu G. Stability of energy gaps under variations of the magnetic field. Lett. Math. Phys. 1986, 11:127. LMPHDY, 0377-9017, 10.1007/BF00398423.
20. 0(X)-algebras. Indiana Univ. Math. J. 1996, 45:463. IUMJAB, 0022-2518, 10.1512/iumj.1996.45.1086.
21. *-algebras. Math. Proc. Cambridge Philos. Soc. 1989, 106:293. MPCPCO, 0305-0041.
22. *-algebras. II. Math. Ann. 1990, 287:595. MAANA3, 0025-5831, 10.1007/BF01446916.
23. *-algebras coming from group cocycles and actions. Math. Ann. 1989, 283:631. MAANA3, 0025-5831, 10.1007/BF01442857.
24. Tomiyama J. Topological representation of C-algebras. Tohoku Math. J. 1962, 14:187. TOMJAM, 0040-8735, 10.2748/tmj/1178244174.
25. Tomiyama J. A characterization of C-algebras whose conjugate spaces are separable. Tohoku Math. J. 1963, 15:96. TOMJAM, 0040-8735, 10.2748/tmj/1178243872.