Some Characterizations of the Properties ■ and LB∞

The aim of this paper is to give some properties of the linear topological invariant ■Using these results we show that a nuclear Fréchet space F has the property LBif and only if everyseparately holomorphic function on an open subset U×V of E×F has a local Dirichlet representation,where E is a nuclear Fréchet space with the property■having a basis.