| Week | Topic | Read | Comments | | |
| 2 | Duality of $\ell^p$-spaces and convergent sequences and sequences converging to zero. $L^p$-spaces for measure spaces. Definition and Completeness, Basics of measure theory, e.g. Fubini's Theorem. Minkowski's Integral Inequality. | Bowers-Kalton: 2.1, 2.2; Lieb-Loss: 2.1 | | | |
| 3 | Hanner's inequality, directional differentiablity of L^p-norms, weak convergence in L^p-spaces, projection theorem for convex sets in L^p-spaces | Read Bowers-Kalton: 2.2, Lieb-Loss: Theorems 2.6, 2.8, 2.10., 2.11, 2.12. | | | |
| 4 | Completeness of L^ p-spaces, definition of weak convergence, Linear functionals separate, lower semicontiuity of norms, the dual of L ^ p | Lieb-Loss: Theorem 2.7, Definition 2.9, Theorem 2.10, Theorem 2.14 | | | |
| 5 | Approximation by smooth functions, Separability of Lebesgue spaces, Banach-Alaoglu for Lebesgue spaces, Zorn's lemma | Theorem 2.16, Lemma 2.17, Theorem 2.18 in Lieb Loss | | | |
| 6 | Hahn-Banach and Banach limits | Bowers-Kalton 3.2 and 3.4 | | | |
| 7 | Norming functionals, canonical embedding, reflexive Banach spaces, adjoint of a bounded operator between Banach spaces, integral operators on Lebesgue spaces, Volterra operator, Schur's test | Bowers-Kalton 3.5 and 3.6 | | | |
| 8 | Annihilator and pre-annhilator and their basic properties, analogs of theorems related to the orthogonal complement of kernel and range of a bounded linear operator and its adjoint, quotient Banach spaces, duals of quotients and subspaces | Bowers-Kalton 3.7 and 3.8 | | | |
| 9 | Baire category theorem, uniform boundedness theorem, Banach-Steinhaus | Bowers-Kalton chapter 4 | | | |
| 10 | Uniform (non-)convergence for Fourier series of continuous functions using Banach-Steinhaus, Fejer/ Dirichlet kernel | Bowers-Kalton chapter 4 | | | |
| 11 | Topological spaces, weak and product topologies, compactness, the weak topology of a normed space | Notes or Folland sections 4.1-4.4, Bowers-Kalton 5.1 and pages 98-100. | | | |
| 12 | weak and weak* topologies | Notes or Bowers-Kalton 5.4 pages 100-105. | | | |