Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces

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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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteNon-Hermitian Hamiltonians in Quantum Physics
Numero di pagine17
Stato di pubblicazionePublished - 2016

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