Lecture 18: The Adjoint 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=BctaYoR9tOY&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=18 We define adjoint operators via the Riesz Representation theorem. This allows us to prove an analogue of the Rank-Nullity theorem for bounded linear operators. Then, we start exploring compact operators a little, which we will soon see are “almost matrices”. 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.