Some characterizations of the properties (DN) and ($\tilde\Omega$) | Zendy

Le Mau Hai | Zendy; Nguyẽn Văn Khuê | Zendy

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Some 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.

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