Nguyen Van Hao and Bui Dac Tac

Abstract

        In this note we prove that the space [\Cal H(O_E)]' is asymptotically normable (resp. has property DN) if E is an asymptotically normable Frechet space (resp. E is a Frechet DN-space)having absolute basis. We also investigate these properties of the space [\Cal H(O_E)]' when K is a balanced compact subset of an asymptotically normable Frechet-Hilbertisable space and K is a polynomially convex conpact set in  Cⁿ.