Classification of nearly invariant subspaces of the backward shift
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- by Eric Hayashi PDF
- Proc. Amer. Math. Soc. 110 (1990), 441-448 Request permission
Abstract:
Let ${S^*}$ denote the backward shift operator on the Hardy space ${H^2}$ of the unit disk. A subspace $M$ of ${H^2}$ is called nearly invariant if ${S^*}h$ is in $M$ whenever $h$ belongs to $M$ and $h(0) = 0$. In particular, the kernel of every Toeplitz operator is nearly invariant. A function theoretic characterization is given of those nearly invariant subspaces which are the kernels of Toeplitz operators, and it is shown that they can be put into one-to-one correspondence with the Cartesian product of the set of exposed points of the unit ball of ${H^1}$ with the set of inner functions.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 441-448
- MSC: Primary 47A15; Secondary 30H05, 47B35, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019277-0
- MathSciNet review: 1019277