Open AccessSome characterizations of the properties (DN) and ($\tilde\Omega$)
Author(s) -
Le Mau Hai,
Nguyẽn Văn Khuê
Publication year - 2000
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14307
Subject(s) - mathematics , omega , combinatorics , compact space , space (punctuation) , equivalence (formal languages) , pure mathematics , physics , linguistics , philosophy , quantum mechanics
The aim of this paper is to show that 7816H_w(B,F) = H(B,F)7816 for every $\mathrm{LB}^\infty$-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 $\mathrm{LB}^\infty$-regular compact set $B$ in a Schwartz-Frechet space $E$ with an absolute basis and the property $(\tilde\Omega)$ also established here.