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Invariant subspaces of perturbed backward shift (2407.17352v2)
Published 24 Jul 2024 in math.FA, math.CV, and math.OA
Abstract: We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of nearly invariant subspaces. Kernels of certain perturbed Toeplitz operators are examples of the newly introduced nearly invariant subspaces.