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arXiv · 2005.12786

Study of nearly invariant subspaces with finite defect in Hilbert spaces

Arup Chattopadhyay·Soma Das
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Abstract

In this article, we briefly describe nearly $T^{-1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space $\mathcal{H}$ as a generalization of nearly $T^{-1}$ invariant subspaces introduced by Liang and Partington in \cite{YP}. In other words we characterize nearly $T^{-1}$ invariant subspaces with finite defect in terms of backward shift invariant subspaces in vector-valued Hardy spaces by using Theorem 3.5 in \cite{CDP}. Furthermore, we also provide a concrete representation of the nearly $T_B^{-1}$ invariant subspaces with finite defect in a scale of Dirichlet-type spaces $\mathcal{D}_\alpha$ for $\alpha \in [-1,1]$ corresponding to any finite Blashcke product $B$.

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Arup Chattopadhyay, Soma Das. 2020-05-26. Study of nearly invariant subspaces with finite defect in Hilbert spaces. https://arxiv.org/abs/2005.12786

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