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

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MIT 18.102 Introduction to Functional Analysis, Spring 2021
Instructor: Dr. Casey Rodriguez

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

  1. MIT OpenCourseWare
  2. Compact operators
  3. eigenvectors
  4. finite-rank operators
  5. resolvent
  6. spectral theory
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Комментарии
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At 42:16, in the blackboard, T = T_0(I - T_0^{-1}(T-T_0) ), but it is typo.
It should be T = T_0(I - T_0^{-1}(T_0-T) )

hausdorffm
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50:35
"I only have a finite amount of time in class" - should be more precisely replased as "I only have a finite measure of time in class" 🤣

broccoloodle
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I miss the days when professors / instructors took pride in their appearance. Not expecting someone to wear a suit (though it's professional-looking), but a wrinkled up shirt?

atlantic_love