Lectures related to Functional Analysis I: November 18, 2021

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores functional spaces, linear applications, sublinear functionals, and the Hahn-Banach theorem.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.