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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 4, 2002, pp. 891–899
DOI: 10.4171/ZAA/1115

Published online: 2002-12-31

Non-Compact $\lambda$-Hankel Operators

Ruben A. Martínez-Avendaño[1] and Peter Yuditskii[2]

(1) Michigan State University, East Lansing, USA
(2) Johannes Kepler University Linz, Austria

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

Keywords: Hankel operators, generalizations, Carleson measures, interpolating sequences

Martínez-Avendaño Ruben, Yuditskii Peter: Non-Compact $\lambda$-Hankel Operators. Z. Anal. Anwend. 21 (2002), 891-899. doi: 10.4171/ZAA/1115