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Kernels of Toeplitz Operators via Bourgain's Factorization Theorem

✍ Scribed by Konstantin M. Dyakonov

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
170 KB
Volume
170
Category
Article
ISSN
0022-1236

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✦ Synopsis

Using Bourgain's factorization theorem, we characterize the subspaces of H p , 1 p , that coincide with the kernels of Toeplitz operators. This is related to (but entirely independent of) earlier work of E. Hayashi. One consequence of our characterization is that, for some inner functions %, the class of uniqueness sets for K p % depends on p; here

%zÄ H p is the star-invariant subspace in H p generated by %. Moreover, a construction is provided of Blaschke products B and b for which the dimension function p [ dim(K p B & bH p ) has prescribed jumps at prescribed points.

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