Weighted Hankel operators and matrices

Abstract

In this paper, the notions of weighted Hankel matrix along withweighted Hankel operator $S_{\phi}^{\beta}$, with $\phi ınL^{ınfty}({\beta})$ on the space $L^2(\beta)$,$\beta=\{\beta_n\}_{nın \Bbb{Z}}$ being a sequence of positivenumbers with $\beta_0=1$, are introduced. It is proved that anoperator on $L^2(\beta)$ is a weighted Hankel operator on$L^2(\beta)$ if and only if its matrix is a weighted Hankel matrix.Various properties of the weighted Hankel operators$S_{\phi}^{\beta}$ on $L^2(\beta)$ are also discussed.