Discrete Cesaro operator between weighted Banach spaces on homogenous trees

Abstract

We introduce discrete Cesaro operator on weighted Banach spaces on homogenous trees. We characterize continuity and compactness of these type of operators acting between weighted Banach spaces on homogenous trees. In particular, we prove that discrete Cesaro operator acting on the Banach space of bounded functions on homogenous trees is always continuous, but it is never compact. However, such an operator acting on weighted Banach spaces of bounded functions on homogenous trees may not be continuous for some weight functions. Moreover, we provide plenty of examples of weight functions such that these type of operators acting on the corresponding weighted Banach spaces of bounded functions on homogenous trees are compact.