G-Riesz dual sequences for g-Bessel sequences

Abstract

Duality principles in Gabor theory play a fundamental role for analyzing Gabor systems. In this paper, we obtain some results of duality principles for g-frames. Let {γj ∈ B(H, Hj) : j ∈ ℕ} and {ηi ∈ B(H, Hi) : i ∈ ℕ} be g-orthonormal bases for H with respect to {Hi}i∈ℕ. For a g-Bessel sequence Λ = {Λi ∈ B(H, Hi) : i ∈ ℕ}, we define [Formula: see text]. Then we describe some properties of the sequence [Formula: see text]. We also characterize the sequence [Formula: see text] when Ψ = {Ψi ∈ B(H, Hi) : i ∈ ℕ} is a dual g-frame of {Λi}i∈ℕ.