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arXiv · 2003.12549

Nearly invariant subspaces for operators in Hilbert spaces

Yuxia Liang·Jonathan R. Partington
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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 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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Yuxia Liang, Jonathan R. Partington. 2020-03-27. Nearly invariant subspaces for operators in Hilbert spaces. https://arxiv.org/abs/2003.12549

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