Functional Analysis I: Foundations and Applications

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

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