Discrete Cesaro operator between weighted Banach spaces on homogenous trees (Q2193477)

This paper studies the discrete Cesàro operator on weighted Banach spaces on homogenous trees. Continuity and compactness are characterized. The discrete Cesàro operator acting on the Banach space of bounded functions on homogenous trees is continuous, but not compact. This operator acting on weighted Banach spaces of bounded functions on homogenous trees may not be continuous for some weight functions. Moreover, examples of weight functions are presented such that the operator acting on the corresponding weighted Banach spaces of bounded functions on homogenous trees is compact.