Non-self-adjoint Hamiltonians defined by generalized Riesz bases

  title={Non-self-adjoint Hamiltonians defined by generalized Riesz bases},
  author={Hiroshi Inoue and Mayumi Takakura},
  journal={Journal of Mathematical Physics},
Bagarello, Inoue, and Trapani [J. Math. Phys. 55, 033501 (2014)] investigated some operators defined by the Riesz bases. These operators connect with quasi-Hermitian quantum mechanics, and its relatives. In this paper, we introduce a notion of generalized Riesz bases which is a generalization of Riesz bases and investigate some operators defined by the generalized Riesz bases by changing the frameworks of the operators defined in the work of Bagarello, Inoue, and Trapani. 
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