A weak Grothendieck compactness principle

作者：Dowling P N^*; Freeman D; Lennard C J; Odell E; Randrianantoanina B; Turett B

来源：Journal of Functional Analysis, 2012, 263(5): 1378-1381.

DOI：10.1016/j.jfa.2012.05.014

• Schur property
• Symmetric basis

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in the closed convex hull of a weakly null sequence if and only if the Banach space has the Schur property.

• 出版日期2012-9-1