Some characterizations of the properties (DN) and ($\tildeΩ$) - Hai, Le Mau; van Khue, Nguyen (Mathematica Scandinavica, 2000)
The aim of this paper is to show that 7816H_w(B,F) = H(B,F)7816 for every $LB^∞$-regular compact set $B$ in a Frechet space $E$ if and only if $F$ is a Frechet space having property (DN). At the same time, the equivalence between the existence of the $LB^∞$-regular compact set $B$ in a Schwartz-Frechet space $E$ with an absolute basis and the property $(\tildeΩ)$ also established here.