Spectral properties and numerical range of off-diagonal infinite-dimensional Hamiltonian operators

Abstract

The spectral properties of the off-diagonal infinite-dimensional Hamiltonian operator are studied in this article. Characterizations of the spectrum, the point spectrum and the residual spectrum are given. A spectral inclusion property of numerical range is proved.

Keywords:

• infinite-dimensional off-diagonal Hamiltonian operator
• point spectrum
• residual spectrum
• numerical range

AMS Subject Classifications::

• 47B47
• 47A12

Acknowledgements

The authors thank the anonymous referee for his/her helpful suggestions. This work is supported by NNSF of China (grant nos 11101200, 10962004, 11061019), NSF of Inner Mongolia (grant No. 2010MS0108) and SPH-IMU (grant No. Z20090103).