Generalized Cesaro tensor and it's properties

Recently, infinite and finite dimensional generalized Hilbert tensors have been introduced. In this paper, the authors further introduce infinite and finite dimensional generalized Cesaro tensors as a generalization of Cesaro matrices and discuss the properties of these structured tensors. Next, some  upper bounds of $Z_{1}$-spectral radius of generalized Cesaro tensors  and  generalized Hilbert tensors are given,  which improves the existing ones. Finally, we obtain conditions under which a generalized Cesaro tensor is column sufficient tensor.