Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-in... YouTube Playlist:    • Lecture 19: Compact Subsets of a Hilbert S...   We show the connection between compact subsets of a Hilbert space and closed, bounded subsets with equi-small tails (a result analogous to the Arzela-Ascoli Theorem). Then, we define finite-rank operators and compact 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.