MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Weighted Hankel operators and matrices
Gopal Datt and Deepak Kumar Porwal

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.

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Keywords: Weighted Hankel matrix; weighted Hankel operator.

MSC: 47B35, 47B20

Pages:  353--363     

Volume  65 ,  Issue  3 ,  2013