Meromorphic functions of uniform type between duals of Fréchet spaces (Q1879120)

The main result is Theorem 3.1: Let \(E\) be a Fréchet space such that \(H(E,\mathbb{C})= H_{ub}(E,\mathbb{C})\) (ub: uniformly bounded type). Then for every Fréchet space \(F\in (DN)\): \(H(E,F)= H_{ub}(E,F)\). Using this result, the author proves the following Theorem 5.1. Let \(E\) be a Fréchet-Montel space, then \(E\in (DN)\) iff for any Fréchet space \(F\) satisfying \(H(F,\mathbb{C})= H_{ub}(F,\mathbb{C})\), every \(F^*\)-valued meromorphic function on \(E^*\) is of bounded type.