Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

Abstract

An investigation is made of the generalized Cesàro operators $$C_t$$ C t , for $$t\in [0,1]$$ t ∈ [ 0 , 1 ] , when they act on the space $$H({{\mathbb {D}}})$$ H ( D ) of holomorphic functions on the open unit disc $${{\mathbb {D}}}$$ D , on the Banach space $$H^\infty $$ H ∞ of bounded analytic functions and on the weighted Banach spaces $$H_v^\infty $$ H v ∞ and $$H_v^0$$ H v 0 with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of $$C_t$$ C t as well as their linear dynamics and mean ergodicity.