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Structure of Kernels and Cokernels of Toeplitz Plus Hankel Operators

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Abstract

Toeplitz plus Hankel operators T(a) + H(b), \({a, b \in L^\infty}\) acting on the classical Hardy spaces H p, \({1< p < \infty}\), are studied. If the generating functions a and b satisfy the so-called matching condition

$$a(t) a(1/t)=b(t) b(1/t),$$

an effective description of the structure of the kernel and cokernel of the corresponding operator is given. The results depend on the behaviour of two auxiliary scalar Toeplitz operators, and if the generating functions a and b are piecewise continuous, more detailed results are obtained.

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Authors and Affiliations

  1. Universiti Brunei Darussalam, Bandar Seri Begawan, BE 1410, Brunei

    Victor D. Didenko

  2. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Bernd Silbermann

Authors
  1. Victor D. Didenko
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  2. Bernd Silbermann
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Correspondence to Bernd Silbermann.

Additional information

This research was carried out when the second author visited the Universiti Brunei Darussalam (UBD). The support of UBD provided via Grant UBD/GSR/S&T/19 is highly appreciated.

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Didenko, V.D., Silbermann, B. Structure of Kernels and Cokernels of Toeplitz Plus Hankel Operators. Integr. Equ. Oper. Theory 80, 1–31 (2014). https://doi.org/10.1007/s00020-014-2170-9

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  • DOI: https://doi.org/10.1007/s00020-014-2170-9

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