On the Generalized Riesz-Dual Sequences in Hilbert Spaces

Abstract

In this paper we define the generalized Riesz-dual sequence from a \( g \)-Bessel sequence with respect to a pair of \( g \)-orthonormal bases as a generalization of the Riesz-dual sequence. We characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract \( g \)-frame setting.