A model operator $H$ associated to a system describing four particles in interaction, without conservation of the number of particles, is considered. We describe the essential spectrum of $H$ by the spectrum of the channel operators and prove the Hunziker-van Winter-Zhislin (HWZ) theorem for the operator $H.$ We also give some variational principles for boundaries of the essential spectrum and interior eigenvalues.
Tulkin H. Rasulov, Mukhiddin I. Muminov, and Mahir Hasanov, On the spectrum of a model operator in Fock space, Methods Funct. Anal. Topology 15
(2009), no. 4, 369-383.
BibTex
@article {MFAT469,
AUTHOR = {Rasulov, Tulkin H. and Muminov, Mukhiddin I. and Hasanov, Mahir},
TITLE = {On the spectrum of a model operator in Fock space},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {4},
PAGES = {369-383},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=469},
}