Non-self-adjoint hamiltonians defined by generalized Riesz bases

Abstract

In \cite{b-i-t}, F. Bagarello, A. Inoue and C. Trapani investigated some operators defined by Riesz bases. These operators connect with $quasi$-$hermitianquantummechanics$, and its relatives. In this paper, we change the frameworks of these operators, and then almost results obtained in \cite{b-i-t} become trivial. Furthermore, we introduce a notion of generalized Riesz bases which is a generalization of Riesz bases and investigate some operators defined by generalized Riesz bases.

Cited by in corpus (6)

• Biorthogonal vectors, sesquilinear forms and some physical operators
• General theory of regular biorthogonal pairs and its physical applications
• Semi-regular biorthogonal pairs and generalized Riesz bases
• Frames and weak frames for unbounded operators
• Generalized Riesz systems and orthonormal sequences in Krein spaces
• Some perturbation results for quasi-bases and other sequences of vectors