Fusion-Riesz frame in Hilbert space
【摘要】：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 fusionRiesz 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.