MIT 18.102 Introduction to Functional Analysis, Spring 2021 - Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=G3mAXHuoDSw&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=4 We prove two more fundamental “theorems with names” as Casey puts it: the Open Mapping Theorem and the Closed Graph Theorem. We conclude with the notion of a Hamel basis for a vector space (finite or infinite dimensional). License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.