Polynomials on Kothe echelon spaces

We give conditions under which the space of n-homogeneous continuous polynomials on a Kothe echelon space, endowed with the topology of uniform convergence on bounded subsets, is barrelled. We also characterize when it is barrelled for every positive integer n in terms of the space order. A characterization of the reflexivity of spaces of homogeneous continuous polynomials on Kothe echelon spaces is also obtained.