Unconditional basis of Banach spaces and Weak*- sequential property

Volume 22 , Issue 2 , December 2020 , Pages 143-148

Authors

Pshtiwan Sabir Nouri 1 ; Mudhafar Fattah Hama 2

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

DOI logo 10.17656/jzs.10815

Keywords

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) ?

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  • Published at20 December 2020

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