jzs-10815

Unconditional basis of Banach spaces and Weak*- sequential property

Pshtiwan Sabir Nouri*1, Mudhafar Fattah Hama2, and Hassan Hussien Ebrahim1

1 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University , Iraq.

2 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Kurdistan Region- Iraq

*Corresponding author’s e-mail: pshtiwanmath6@gmail.com, 2mudhafar.hama@univsul.edu.iq

Original: 9 April 2020        Revised: 1 May 2020        Accepted: 23 August 2020        Published online: 20 December 2020

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Abstract

 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) ?

Key Words:  unconditional basis, Weak*-sequential

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