Left invertibility of formal Hamiltonian operators

Abstract

In this paper, we investigate the left invertible completion of the formal Hamiltonian operators with unbounded entries. In particular, the left invertible completion of Hamiltonian cases is also given. Based on the space decomposition technique, the sufficient and necessary conditions are given according to whether the dimension of is finite or infinite.

Keywords:

• formal Hamiltonian operator
• left invertibility
• completion

AMS Subject Classifications:

• 47A10
• 47A55

Acknowledgements

We are grateful to the referees for their valuable comments on this paper.

Notes

This work is partially supported by the National Natural Science Foundation of China [grant number 1061019], [grant number 11261034], [grant number 11371185]; the Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20111501110001]; the ‘Chunhui Program’ of the Ministry of Education of China [grant number Z2009-1-01010]; the Major Program of the Natural Science Foundation of Inner Mongolia [grant number 2013ZD01]; the Natural Science Foundation for Fostering Distinguished Young Scholars of Inner Mongolia [grant number 013JQ01] and the Program for Young Talents of Science and Technology in Universities of Inner Mongolia [grant number NJYT-12-B06].