Advanced Analysis – Siena

Argomenti del programma: Recalls on topological spaces, metric spaces, Banach spaces and Hilbert spaces The Hahn-Banach Theorems. Introduction to the theory of conjugate convex functions. The uniform boundedness principle and the closed graph theorem. Weak topology and weak* topology . Reflexive spaces. Separable spaces. Uniform convexity. Linear and continuous operators Compact operators. Operators in Hilbert spaces. Hille- Yosida Theorem.