Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every ω-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrödinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.
Bellomonte, G. (2016). Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces. In F. Bagarello, R. Passante, C. Trapani (a cura di), Non-Hermitian Hamiltonians in Quantum Physics (pp. 167-183). Springer Science and Business Media, LLC [10.1007/978-3-319-31356-6_11].
Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces
BELLOMONTE, Giorgia
2016-01-01
Abstract
Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every ω-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrödinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.File | Dimensione | Formato | |
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