MIT 18.102 Introduction to Functional Analysis, Spring 2021 - Lecture 5: Zorn’s Lemma and the Hahn-Banach 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=KlAjiDivJoQ&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=5 A first application of Zorn’s lemma is the existence of a Hamel basis. We then introduce the very useful Hahn-Banach theorem, which states that a bounded linear functional on a subspace can be continuously extended to the entire normed space. 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.