Quasinormable spaces of poynomials

Abstract

Let E be a Fréchet space and p( n E) the space of n-homogeneous continuous polynomials on E, endowed with topology τ b of uniform convergence on the bounded subsets of E. The author gives an example of a Fréchet space E such that (p( n E),τ b ) is quasinormable and all the natural topologies are different for n≥2.