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Classification of Nearly Invariant Subspaces of the Backward Shift

1990
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Proceedings of the American Mathematical Society
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Let 5 denote the backward shift operator on the Hardy space H of the unit disk. A subspace M of H 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

doi:10.2307/2048087
fatcat:wzksgc2sbnaifodm6um7jkwk6u