Abstract
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.
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We would like to thank the referees for their helpful comments and suggestions.
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Supported by National Natural Science Foundation of China (Grant Nos. 11671201 and 11571247)
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Liu, A.F., Li, P.T. K-fusion Frames and the Corresponding Generators for Unitary Systems. Acta. Math. Sin.-English Ser. 34, 843–854 (2018). https://doi.org/10.1007/s10114-017-7196-x
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DOI: https://doi.org/10.1007/s10114-017-7196-x