On the fine spectrum of the Cesàro operator in c₀

Abstract

In the present paper, the fine spectrum of the Cesàro operator in the sequence space c₀ has been examined. Although the discussion is made for determination of the spectrum of the Cesàro operator in the sequence space c₀ by Reade [14] and the others, our consequences are more refinement and include a remark concerning with the previous works. Further, a Mercerian theorem has also been given. Finally, the fine spectrum of the Cesàro operator in the sequence space c has been given, without proof.