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Construct approximate dual g-frames in Hilbert spaces. (English) Zbl 1459.42043

Summary: In this paper, we first present some simple approaches to obtain dual and approximate dual g-frames. Then, we show that approximate dual g-frames are stable under some conditions. Finally, we give mainly a new characterization for approximate dual g-frames associated with given g-frames and bounded operators. Moreover, we prove that if two g-frames are close to each other, then we can find approximate dual g-frames associated with them which are close to each other.

MSC:

42C15 General harmonic expansions, frames
47B38 Linear operators on function spaces (general)
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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