MR3785684 Reviewed Liu, Ai Fang(PRC-NAA); Li, Peng Tong(PRC-NAA) K-fusion frames and the corresponding generators for unitary systems. (English summary) Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 5, 843–854. 42C15 (47D03)

Abstract

Given an operator K∈B(H), in this paper the authors introduce K-fusion frames as a generalization of fusion frames, defined as a sequence {Wi} of closed subspaces of the Hilbert space H. For K=1, this becomes a fusion frame. They prove some properties of K-fusion frames, based on considering the operator K and the frame operators. In the last section, for a unitary system U, the authors define a K-fusion frame generator in a way similar to the frame vectors for unitary systems. Some properties and characterization theorems are derived for operators in the generalized local commutant of U.