Le Mau Hai

Abstract

     It is shown that every holomorphic function on a nuclear Frechet space E with values in a Frechet space F is of uniform type if E has the linear topological invariant (\widetilde Ω) and F has the linear topological invariant (DN) respectively. Based on the obtained result the equivalence of the holomorphicity and the weak holomorphicity of Frechet-valued functions on  L-regular compact subsets in a nuclear Frechet space is established.