Classification of nearly invariant subspaces of the backward shift

Author:
Eric Hayashi

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

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Abstract: Let denote the backward shift operator on the Hardy space of the unit disk. A subspace of is called nearly invariant if is in whenever belongs to and . 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 with the set of inner functions.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1019277-0

Article copyright:
© Copyright 1990
American Mathematical Society