On the Property (LB¥) of Spaces of Germs of Holomorphic Functions and the Properties (\widetilde W, \overline W) of the Hartogs Domain in Infinite Dimension

Le Mau Hai and Pham Hien Bang

Abstract

        The aim of this paper is to establish the property LB¥ on [H(Ke)]' under the assumption that E is a Frechet space with an absolute basis and  Ke is a balanced convex compact subset of E. At the same time, the properties (\widetilde W, \overline W) for the Hartogs domains associated to an open polydisc in a nuclear Frechet space with a basis will be also proved.