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Products of Hankel operators

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Abstract

This paper studies products of Hankel operators on the Hardy space. We show thatH σ(1)* f H fσ(2) H σ(3)* f =0 for all permutation σ if and only if eitherH f1 orH f2 orH f3 is zero. Using Douglas' localization theorem and Izuchi's theorem on Sarason's three functions problem, we show that

$$H^\infty [f] \cap H^\infty [g] \cap H^\infty [h] \subset H^\infty + C$$

is a sufficient condition forH *f H g H *h ,H *g H f H *h , andH *f H h H *g to be compact.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN

    Daoxing Xia & Dechao Zheng

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  1. Daoxing Xia
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  2. Dechao Zheng
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Additional information

This work was partly supported by NSF grants. The second author was also partly supported by the Research Council of Vanderbilt University.

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Xia, D., Zheng, D. Products of Hankel operators. Integr equ oper theory 29, 339–363 (1997). https://doi.org/10.1007/BF01320706

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  • DOI: https://doi.org/10.1007/BF01320706

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