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<p>We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to characterize 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.</p>

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Invariant Subspaces of Perturbed Backward Shift

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Soma Das,
  • Jaydeb Sarkar

摘要

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to characterize 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.