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g-Riesz dual sequences for g-Bessel sequences
https://doi.org/10.1142/S1793557114500417Cited by:7 (Source: Crossref)
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 
. Then we describe some properties of the sequence 
. We also characterize the sequence 
when Ψ = {Ψi ∈ B(H, Hi) : i ∈ ℕ} is a dual g-frame of {Λi}i∈ℕ.
AMSC: 42C15, 42A38, 41A58
