JournalszaaVol. 21, No. 4pp. 891–899

Non-Compact λ\lambda-Hankel Operators

  • Ruben A. Martínez-Avendaño

    Michigan State University, East Lansing, USA
  • Peter Yuditskii

    Johannes Kepler University Linz, Austria
Non-Compact $\lambda$-Hankel Operators cover
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Abstract

A λ\lambda-Hankel operator XX is a bounded operator on Hilbert space satisfying the operator equation SXXS=λXS*X–XS = \lambda X, where SS is the (unilateral) forward shift and SS* is its adjoint. We prove that there are non-compact λ\lambda-Hankel operators for λ\lambda 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 λ\lambda-Hankel operator associated with the Carleson measure given by the interpolating sequence is non-compact.

Cite this article

Ruben A. Martínez-Avendaño, Peter Yuditskii, Non-Compact λ\lambda-Hankel Operators. Z. Anal. Anwend. 21 (2002), no. 4, pp. 891–899

DOI 10.4171/ZAA/1115