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The kernel of a Toeplitz operator

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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

  1. Bloomfield, P. B., Jewell, N. P., and Hayashi, E., Characterizations of completely nondeterministic stochastic processes, Pacific J. Math., 107 (1983), 307–317.

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  2. Hayashi, E., The solution sets of extremal problems in H1, Proc. Am. Math. Soc., 93 (1985), 690–696.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, 1600 Holloway Ave., 94132, San Francisco, CA

    Eric Hayashi

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  1. Eric Hayashi
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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

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