Open Access

# On the spectrum of a model operator in Fock space

### Abstract

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.

### Article Information

 Title On the spectrum of a model operator in Fock space Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 4, 369-383 MathSciNet MR2603835 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

Tulkin H. Rasulov
Department of Physics and Mathematics, Samarkand State University, 15 University Boulevard, Samarkand, 140104, Uzbekistan

Mukhiddin I. Muminov
Department of Physics and Mathematics, Samarkand State University, 15 University Boulevard, Samarkand, 140104, Uzbekistan

Mahir Hasanov
Southern Alberta Institute of Technology, 1301 16th Ave NW Calgary, Alberta, Canada T2M 0L4

### Citation Example

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},
}