
Let (X,\(\Sigma\),m) be a complete \(\sigma\)-finite measure space, and let T be a \(\Sigma\)-measurable mapping in X such that \(m\circ T^{-1}\) is absolutely continuous with respect to m. The corresponding weighted composition operator W on \(L^ 2(X,\Sigma,m)\) generated by the weight function \(\phi\) is defined by \(Wf:=\phi f\circ T\). A measure theoretic characterization of hyponormality for such operators is given. This generalizes a result of \textit{D. Harrington} and \textit{R. Whitley} [J. Oper. Theory 11, 125-135 (1984; Zbl 0534.47017)], who considered the case of unweighted composition operators (i.e. \(\phi =1)\). An example illuminating the connection to isometries is given.
weighted composition operator, Linear operators on function spaces (general), Subnormal operators, hyponormal operators, etc., hyponormality
weighted composition operator, Linear operators on function spaces (general), Subnormal operators, hyponormal operators, etc., hyponormality
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