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R-duality in g-frames. (English) Zbl 1369.42022

Summary: Recently, the concept of g-Riesz dual sequences for g-Bessel sequences has been introduced. In this paper, we investigate under what conditions a g-Riesz sequence \(\Phi=\{\Phi_j\in L(H,H_j):j\in \mathcal I\}\) is the g-Riesz dual sequence of a given g-frame \(\Lambda=\{\Lambda_i\in L(H,H_i):i\in \mathcal I\}\).

MSC:

42C15 General harmonic expansions, frames
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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