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Non-self-adjoint hamiltonians defined by generalized Riesz bases (1604.00161v1)
Published 1 Apr 2016 in math-ph and math.MP
Abstract: In \cite{b-i-t}, F. Bagarello, A. Inoue and C. Trapani investigated some operators defined by Riesz bases. These operators connect with ${\it quasi}$-${\it hermitian \; quantum \; mechanics}$, 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.
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