A Complete Aak-theorem for Weighted Sequence Spaces
نویسنده
چکیده
Abstract. We give a full extension of (one version of) the celebrated "AAK-theorem" on Hankel operators, to the case of weighted l-spaces with increasing weights. This theorem was conjectured in [3], and it improves earlier work by S. Treil and A. Volberg, [8]. We also show that the corresponding extension of the classical formulation of the "AAK-theorem" fails, and show that this is a consequence of the failure of a sharp version of Nehari’s theorem in this setting. We also note that a weaker version of Nehari’s theorem was proven in [8], and hence this theorem can not be improved.
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