Abstract

In this paper, the notions of weighted Hankel matrix along with weighted Hankel operator $S_{\phi}^{\beta}$, with $\phi \in L^{\infty}({\beta})$ on the space $L^2(\beta)$, $\beta=\{\beta_n\}_{n\in \Bbb{Z}}$ being a sequence of positive numbers with $\beta_0=1$, are introduced. It is proved that an operator 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.

Keywords: Weighted Hankel matrix; weighted Hankel operator.

MSC: 47B35, 47B20

Pages:  353$-$363     

Volume  65 ,  Issue  3 ,  2013