Study of nearly invariant subspaces with finite defect in Hilbert spaces

2020/05/26 by Arup Chattopadhyay, Soma Das, Chattopadhyay, Arup +1 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2005.12786

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 H as a generalization of nearly T^-1 invariant subspaces introduced by Liang and Partington in \citeYP. 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 \citeCDP. 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 D_α for α∈ [-1,1] corresponding to any finite Blashcke product B.

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• Perturbations of Toeplitz operators on vector-valued Hardy spaces

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