Unconditional basis of Banach spaces and Weak*- sequential property - Nouri, Pshtiwan Sabir; Hama, Mudhafar Fattah (Sulaimani Journal for Pure and Applied Sciences, 2020)
The main purpose of this article is to answer the Plichko's question; let X be any Banach space and Γ⊂X* be any total set if Ba(X; σ(X; Γ)) =Ba(X; weak); then does imply every weakly* sequentially closed sub-space of X* is weakly* closed? Also, answer the question: Let A ⊆X* such that A is convex and bounded and for each element a ∈ \overline{A}weak* then a ∈ \overline{B}weak* for a countable subset B of A; Then does it imply (X; σ(X; Γ)) =Ba(X;weak) ?
Keywords: unconditional basis; Weak*-sequential