Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space

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=SFDMFbzCsH0&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=20 We show that compact operators are precisely limits of finite-rank operators. Then, we define invertible linear operators and begin exploring our final unit of the course: spectral theory for bounded linear operators. 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.