In this paper we discuss some results on non self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that their eigenvectors form Riesz bases of a certain Hilbert space. Also, we exhibit a generalization of those results to the case of rigged Hilbert spaces, and we also consider the problem of the factorization of the aforementioned Hamiltonians in terms of generalized lowering and raising operators.
Bagarello Fabio / Bellomonte Giorgia (2018). On non-self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces. In Topological Algebras and their Applications. Proceedings of the 8th International Conference on Topological Algebras and their Applications, 2014. [10.1515/9783110413557-003].
On non-self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces
Bagarello Fabio
;Bellomonte Giorgia
2018-01-01
Abstract
In this paper we discuss some results on non self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that their eigenvectors form Riesz bases of a certain Hilbert space. Also, we exhibit a generalization of those results to the case of rigged Hilbert spaces, and we also consider the problem of the factorization of the aforementioned Hamiltonians in terms of generalized lowering and raising operators.
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