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

The Frechet sequence spaces ces(p+) are very different to the Frechet sequence spaces p+,1p<, 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 Cesaro 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 Mc(ces(p+)) consisting of the compact multiplier operators are independent of p. Moreover, Mc(ces(p+)) can be topologized so that it is the strong dual of the Frechet-Schwartz space ces(1+) and (Mc(ces(p+))similar or equal to ces(1+) is a proper subspace of the Kothe echelon Frechet space M(ces(p+))=(A),1p<, for a suitable matrix A.