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

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.