The number of weakly compact sets which generate a Banach space

TL;DR

This paper investigates the cardinal invariant CG(X), representing the minimal number of weakly compact sets needed to generate a Banach space, exploring its properties, behavior under subspaces, and connections with the Lindelöf number.

Contribution

It introduces and analyzes the invariant CG(X), providing new insights into its behavior and relationships within Banach space theory.

Findings

CG(X) relates to the Lindelöf number in the weak topology

Behavior of CG(X) under subspace formation is characterized

New questions about the structure of weakly compact generating sets are posed

Abstract

We consider the cardinal invariant CG(X) of the minimal number of weakly compact subsets which generate a Banach space X. We study the behavior of this index when passing to subspaces, its relation with the Lindelof number in the weak topology and other related questions.