Abstract
Extensions of the Hardy and the Bergman modules over the disc algebra are studied. The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators. In the context of function theory, an explicit formula of Ext(L 2α (D), H 2(D)) is obtained. Finally, it is also proved that Ext(L 2α (D), L 2α (D)) ≠ 0. This may be the essential difference between the Hardy and the Bergman modules over the disk algebra.
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Project supported by the National Natural Science Foundation of China and Mathematics Center of the Ministry of Education of China, and the Laboratory of Mathematics for Nonlinear Model and Methods at Fudan University.
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Guo, K. Extensions of Hilbert Modules and Hankel Operators. Chin. Ann. of Math. 21, 17–24 (2000). https://doi.org/10.1007/BF02731953
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DOI: https://doi.org/10.1007/BF02731953