Abstract
The classical Adamjan-Arov-Krein (A-A-K) theorem relating the singular numbers of Hankel operators to best approximations of their symbols by rational functions is given an abstract version. This provides results for Hankel operators acting in weightedH 2(T; μ), as well as inH 2(T d), and an A-A-K type extension of Sarason's interpolation theorem. In particular, it is shown that all compact Hankel operators inH 2(T d) are zero.
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Author partially supported by NSF grant DMS89-11717.
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Cotlar, M., Sadosky, C. Abstract, weighted, and multidimensional Adamjan-Arov-Krein theorems, and the singular numbers of Sarason commutants. Integr equ oper theory 17, 169–201 (1993). https://doi.org/10.1007/BF01200217
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DOI: https://doi.org/10.1007/BF01200217