| Week | Material | Description | |
| week 2 | Chapter 1 in Bowers & Kalton | Normed & metric spaces. Banach spaces. Bounded operators. Dual space.Topology. | |
| week 3 | Chapter 2 in Bowers & Kalton | Examples of Banach spaces. Sequence spaces and their dual. Function spaces. Riesz represnetation theorem. | |
| week 4 | Chapter 2 in Bowers & Kalton | Examples of Banach spaces. Sequence spaces and their dual. Function spaces. Riesz represnetation theorem. | |
| week 5 | Chapter 3 in Bowers & Kalton | Hahn-Banach general, normed and complex case, proof. | |
| week 6 | Chapter 3 in Bowers & Kalton | Applications Hahn-Banach: Haar measure of compact abelian groups. Natural embedding, reflexive spaces. The adjoint of an operator. Quotients and direct sums. | |
| week 7 | Chapter 4 in Bowers & Kalton | Theorem of Baire, Uniform Boundedness Principle, strong contrapostive formulation of the Uniform Boundedness Principle, Banach-Steihnhaus theorem. | |
| week 8 | Chapter 4 in Bowers & Kalton | Existence of divergent Fourier series, Open mapping theorem, Bounded inverse theorem. | |
| week 9 | Chapter 4 & 5 in Bowers & Kalton | Closed graph theorem. Aplications Bounded Inverse Theorem. Vector topological spaces. | |
| week 10 | Chapter 5 in Bowers & Kalton | Convex and locally convex spaces. Hahn-Banach separation Theorem. | |
| week 11 | Chapter 5 in Bowers & Kalton | Seminorm. Minkowski functional. The weak topology. | |
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