Operators on the Fréchet sequence spaces ces(p+) , 1 ≤ p < ∞

The Fréchet sequence spaces $ces(p+)$ are very different to the Fréchet sequence spaces $ell_{p+}$, 1 ≤ p < ∞, that generate them, (Albanese et al. in J Math Anal Appl 458:1314–1323, 2018). The aim of this paper is to investigate various properties (eg. continuity, compactness, mean ergodicity) of certain linear operators acting in and between the spaces ces(p+), such as the Cesàro operator, inclusion operators and multiplier operators. Determination of the spectra of such classical operators is an important feature. It turns out that both the space of multiplier operators M(ces(p+)) and its subspace M_c(ces(p+)) consisting of the compact multiplier operators are independent of p.