On sum and stability of g-frames in Hilbert spaces |
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Authors: | Dongwei Li Tingzhu Huang Guomin Sun |
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Institution: | School of Mathematical Sciences, University of Electronic Science and Technology of China, P.R. China. |
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Abstract: | In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations. |
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Keywords: | Frame g-frame tight g-frame stability |
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