Lectures related to Banach–Alaoglu theorem

Explores advanced analysis topics, including Cauchy sequences, Banach spaces, and the Cauchy-Lipschitz theorem.

Explores the implications of Baire Theorem in functional analysis and metric spaces.

Introduces linear and bounded operators, compact operators, and the Banach space.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Discusses interpreting convergence plots in optimization, identifying bugs based on convergence rates, and understanding optimization algorithms.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.