Abstract
For a shift operator T with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly \(T^{-1}\) invariant subspaces in Hilbert space in terms of invariant subspaces under the backward shift. Going further, given any finite Blaschke product B, we give a description of the nearly \(T_{B}^{-1}\) invariant subspaces for the operator \(T_B\) of multiplication by B in a scale of Dirichlet-type spaces.
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Acknowledgements
This work was done while Yuxia Liang was visiting the University of Leeds. She is grateful to the School of Mathematics at the University of Leeds for its warm hospitality. Yuxia Liang is supported by the National Natural Science Foundation of China (Grant No. 11701422).
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Communicated by Isabelle Chalendar.
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Liang, Y., Partington, J.R. Nearly Invariant Subspaces for Operators in Hilbert Spaces. Complex Anal. Oper. Theory 15, 5 (2021). https://doi.org/10.1007/s11785-020-01050-x
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DOI: https://doi.org/10.1007/s11785-020-01050-x