Some Characterizations of the Properties $$ {\widetilde{{LB}}}^{\infty }$$ and LB ∞

Abstract

The aim of this paper is to give some properties of the linear topological invariant \( {\widetilde{{LB}}}^{\infty }.\) Using these results we show that a nuclear Frechet space F has the property LB∞ if and only if every separately holomorphic function on an open subset U × V of E × F* has a local Dirichlet representation, where E is a nuclear Frechet space with the property \( {\widetilde{{LB}}}^{\infty }\)having a basis.