On sequences not enjoying Schur’s property

Abstract

Here we proved the existence of a closed vector space of sequences - any nonzero element of which does not comply with Schur’s property, that is, it is weakly convergent but not norm convergent. This allows us to find similar algebraic structures in some subsets of functions.

Keywords

• schur property
• weakly convergent sequence
• analytic function
• 40a05
• 20g43
• 15a03