A -Hankel operator is a bounded operator on Hilbert space satisfying the operator equation , where is the (unilateral) forward shift and is its adjoint. We prove that there are non-compact -Hankel operators for a complex number of modulus less than 2, by first exhibiting a way to obtain bounded solutions to the above equation by associating to it a Carleson measure. We then show that an interpolating sequence can be given such that the -Hankel operator associated with the Carleson measure given by the interpolating sequence is non-compact.
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Ruben A. Martínez-Avendaño, Peter Yuditskii, Non-Compact -Hankel Operators. Z. Anal. Anwend. 21 (2002), no. 4, pp. 891–899DOI 10.4171/ZAA/1115