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Two questions on products of Hankel operators. (Chinese. English summary) Zbl 1487.47047

Summary: Suppose that \(f, u\) and \(g\) are in the Hardy space of the unit circle \(H^2\), and \(h\) is a square integrable function on the unit circle. \(H_{\bar f}, H_{\bar u}, H_{\bar g}\) and \(H_h\) are Hankel operators which take the Hardy space of the unit circle \(H^2\) into the orthogonal complement of the Hardy space \((H^2)^\bot\). We obtain the necessary and sufficient conditions for \(H_{\bar f} H^*_{\bar u} H_{\bar g} = H_h\) and \(H_{\bar f} H^*_{\bar u} H_{\bar g} = H_{\bar g} H^*_{\bar u} H_{\bar f}\), respectively.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H10 Hardy spaces
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