K-fusion Frames and the Corresponding Generators for Unitary Systems
Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.
KeywordsK-fusion frame K-fusion frame generator wandering subspace unitary system
MR(2010) Subject Classification42C15 47D03
Unable to display preview. Download preview PDF.
We would like to thank the referees for their helpful comments and suggestions.
- Dai, X., Larson, D.: Wandering vectors for unitary systems and orthogonal wavelets. Mem. Amer. Math. Soc., 134, no. 640 (1998)Google Scholar
- Han, D., Larson, D.: Frames, bases and group representation. Mem. Amer. Math. Soc., 147, no. 697 (2000)Google Scholar