Uniqueness of Unconditional Basis in Banach Spaces: Overview and Recent Advances

A 20-minute conference talk that provides an overview of the uniqueness of unconditional basis in Banach spaces, covering historical developments from the 1930s to recent advances. Delivered by Jose Ansorena at the Workshop on "Structures in Banach Spaces" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in March 2025. Explore the fundamental concepts and significant progress in determining the existence and uniqueness of unconditional basis, a crucial topic within the study of lattice structures in separable Banach and quasi-Banach spaces.