Generic Properties of Contractions on Banach Spaces - Recent Results

Explore a 45-minute mathematics lecture examining the typical properties of operators in the closed unit ball of continuous linear operators on separable Banach spaces, particularly focusing on ℓp-spaces. Delve into the study of natural topologies on the algebra of continuous linear operators, and understand how these transform the closed unit ball into a Polish space. Learn about recent developments related to the Invariant Subspace Problem, specifically investigating whether typical contractions on ℓp spaces possess non-trivial invariant subspaces. Benefit from collaborative research findings presented by Sophie Grivaux, conducted jointly with Étienne Matheron and Quentin Menet. Recorded at the Centre International de Rencontres Mathématiques during the thematic meeting on "Operators on analytic function spaces," the lecture includes chapter markers, keywords, abstracts, and bibliographies for enhanced learning accessibility.