Abstract
Let Tu be a Toeplitz operator on H2 of the unit disk. If the kernel of Tu is non-trivial, it equals g(H2 ⊝ zbH2) where g is an outer function and where b is inner. Moreover, f→gf is an isometry of H2 ⊝ zbH2 onto Ker Tu.
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References
Bloomfield, P. B., Jewell, N. P., and Hayashi, E., Characterizations of completely nondeterministic stochastic processes, Pacific J. Math., 107 (1983), 307–317.
Hayashi, E., The solution sets of extremal problems in H1, Proc. Am. Math. Soc., 93 (1985), 690–696.
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Hayashi, E. The kernel of a Toeplitz operator. Integr equ oper theory 9, 588–591 (1986). https://doi.org/10.1007/BF01204630
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DOI: https://doi.org/10.1007/BF01204630