Basic Concepts in Modern Analysis
Time and Place
יום ב 16:00 - 14:00
יום ה 15:00 - 13:00 בבנין 90 (מקיף ז’)  חדר 136
Banach spaces and Hilbert spaces. Basic properties of Hilbert spaces. Topological vector spaces. Banach-Steinhaus theorem; open mapping theorem and closed graph theorem. Hahn-Banach theorem. Duality. Measures on locally compact spaces; the dual of . Weak and weak- topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. The Stone-Weierstrass theorem. Compact operators on Hilbert space. Introduction to Banach algebras and Gelfand theory. Additional topics as time permits.