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G-frames and g-frame sequences in Hilbert spaces
Authors:Yan Jin Wang  Yu Can Zhu
Institution:(1) Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong;(2) Center of Computational and Theoretical Physics, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong;(3) Department of Mathematics, University of Hong Kong, Hong Kong, Hong Kong
Abstract:In this paper, we first determine the relations among the best bounds A and B of the g-frame, the g-frame operator S and the pre-frame operator Q and give a necessary and sufficient condition for a g-frame with bounds A and B in a complex Hilbert space. We also introduce the definition of a g-frame sequence and obtain a necessary and sufficient condition for a g-frame sequence with bounds A and B in a complex Hilbert space. Lastly, we consider the stability of a g-frame sequence for a complex Hilbert space under perturbation.
Keywords:frame  g-Bessel sequence  g-frame  g-frame sequence
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