Weighted Hankel operators and matrices

Abstract

In this paper, the notions of weighted Hankel matrix along withweighted Hankel operator $S_{\varphi }^{\beta }$, with $\varphi ın{L}^{ınfty}(\beta )$ on the space $L^2(\beta )$,$\beta =\{{\beta }_n{\}}_{nın\mathbb{Z}}$ 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$S_{\varphi }^{\beta }$ on $L^2(\beta )$ are also discussed.