Operator-weighted scalability of fusion frames
摘要
In this paper, we adopt an operator-weighted approach to address the scalability issue in the fusion frames. By introducing relay operators connecting the subspaces and the auxiliary Hilbert spaces, we show that non-scalable fusion frames can be transformed into Parseval R-fusion frames. We analyze the boundedness and compactness of the global relay operator, laying a theoretical basis for the construction of R-fusion frames. Additionally, several construction methods for Parseval R-fusion frames using operator-weighted techniques are proposed. Moreover, we establish precise characterizations by relating the analysis operator of a fusion frame to the domain and injectivity of the global relay operator, which reveals the interplay between the relay operators and the underlying fusion frame structure.