Abstract
The generalized Cesàro operators Ct, for t∈[0,1), introduced in the 1980's by Rhaly, are natural analogues of the classical Cesàro averaging operator C1 and act in various Banach sequence spaces X⊆CN0. In this paper we concentrate on a certain class of Banach lattices for the coordinate-wise order, which includes all separable, rearrangement invariant sequence spaces, various weighted c0 and ℓp spaces and many others. In such Banach lattices X the operators Ct, for t∈[0,1), are always compact (unlike C1) and a full description of their point, continuous and residual spectrum is given. Estimates for the operator norm of Ct are also presented.
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