On q- Cesàro Operators: Boundedness, Compactness and Spectra

The main purpose of the paper is to investigate the spectra of the Cesàro operator C_q, where 0<q<∞, on Banach spaces. For 0<q<1, the method of the proof is to exhibit a relationship between the operator C_q and a generalized difference operator Δ_ab. Furthermore, for 1<q<∞, it is shown that the operator C_q is compact on certain Banach spaces. In this case, the spectra of C_q are completely determined.