Fusion-Riesz frame in Hilbert space |
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Authors: | Xue-bin Li Shou-zhi Yang |
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Institution: | Department of Mathematics, Shantou University, Shantou 515063, China |
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Abstract: | Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame. |
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Keywords: | fusion-Riesz frame Riesz frame of subspace Riesz frame exact fusion frame |
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