Non-self-adjoint Hamiltonians defined by generalized Riesz bases.

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. [ABSTRACT FROM AUTHOR]