# Operator Theory

- Institution: IIT Hyderabad
- Department: Mathematics
- Teacher: Prof. G. Ramesh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106160)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106160)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Semi Inner product spaces](https://invisiblenetwork.ai/learn/nptel/111106160/7fd4f849d7e2) (Video)
2. [Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111106160/ec1c8ef7923d) (Video)
3. [Parallelogram law](https://invisiblenetwork.ai/learn/nptel/111106160/0d87fcb14108) (Video)
4. [Hilbert Spaces](https://invisiblenetwork.ai/learn/nptel/111106160/6206c343107d) (Video)
5. [Orthogonality](https://invisiblenetwork.ai/learn/nptel/111106160/e227c731ae6d) (Video)
6. [Projection Theorem](https://invisiblenetwork.ai/learn/nptel/111106160/49470b069800) (Video)
7. [Linear Operator](https://invisiblenetwork.ai/learn/nptel/111106160/ddb31f3f3f94) (Video)
8. [Bounded Operators](https://invisiblenetwork.ai/learn/nptel/111106160/165bae0a4756) (Video)
9. [Norm of a linear operator](https://invisiblenetwork.ai/learn/nptel/111106160/656271129b5d) (Video)
10. [Examples of bounded operators](https://invisiblenetwork.ai/learn/nptel/111106160/9563b3378f04) (Video)
11. [The Adjoint Operator](https://invisiblenetwork.ai/learn/nptel/111106160/0632d69fce55) (Video)
12. [The adjoint: Properties](https://invisiblenetwork.ai/learn/nptel/111106160/2557c383da0d) (Video)
13. [Closed range operators-1](https://invisiblenetwork.ai/learn/nptel/111106160/42aa759bc41e) (Video)
14. [Closed range operators-2](https://invisiblenetwork.ai/learn/nptel/111106160/19dfaa5f9823) (Video)
15. [Self-adjoint Operators](https://invisiblenetwork.ai/learn/nptel/111106160/4dd74f5232df) (Video)
16. [Normal operators](https://invisiblenetwork.ai/learn/nptel/111106160/32400ec976eb) (Video)
17. [Isometris and Unitaries](https://invisiblenetwork.ai/learn/nptel/111106160/6cd9939035b5) (Video)
18. [Isometris and Unitaries](https://invisiblenetwork.ai/learn/nptel/111106160/ae89949cf216) (Video)
19. [Mutually Orthogonal Projections](https://invisiblenetwork.ai/learn/nptel/111106160/f82396a058ea) (Video)
20. [Invariant Subspaces](https://invisiblenetwork.ai/learn/nptel/111106160/0accc8db1449) (Video)
21. [Monotone Convergence Theorem](https://invisiblenetwork.ai/learn/nptel/111106160/428e065a080d) (Video)
22. [Square root](https://invisiblenetwork.ai/learn/nptel/111106160/ebc7aecdfac1) (Video)
23. [Polar decomposition](https://invisiblenetwork.ai/learn/nptel/111106160/9197eed91938) (Video)
24. [Invertibility](https://invisiblenetwork.ai/learn/nptel/111106160/7dee0ca4f39f) (Video)
25. [Spectrum](https://invisiblenetwork.ai/learn/nptel/111106160/bca664962618) (Video)
26. [Spectral Mapping Theorem](https://invisiblenetwork.ai/learn/nptel/111106160/ea2623b5a0fa) (Video)
27. [Decomposition of spectrum](https://invisiblenetwork.ai/learn/nptel/111106160/607a80de5c0c) (Video)
28. [Computing spectrum: Examples](https://invisiblenetwork.ai/learn/nptel/111106160/aa85643b8cde) (Video)
29. [Approximate spectrum](https://invisiblenetwork.ai/learn/nptel/111106160/ce89c4edf368) (Video)
30. [Approximate spectrum: Properties](https://invisiblenetwork.ai/learn/nptel/111106160/1368fae78d69) (Video)
31. [Numerical bounds](https://invisiblenetwork.ai/learn/nptel/111106160/3c26f2481038) (Video)
32. [Compact Operators](https://invisiblenetwork.ai/learn/nptel/111106160/cdd48f09e248) (Video)
33. [Compact Operators; Properties](https://invisiblenetwork.ai/learn/nptel/111106160/0c2a4cbe2b5e) (Video)
34. [Spectral Theorem: Compact Self-Adjoint Operators](https://invisiblenetwork.ai/learn/nptel/111106160/a8485e0ab1ea) (Video)
35. [Spectral Theorem: Consequences](https://invisiblenetwork.ai/learn/nptel/111106160/7f174b02793f) (Video)
36. [Compact Normal Operators](https://invisiblenetwork.ai/learn/nptel/111106160/943206bf8e82) (Video)
37. [Compact Operators Singular value Decomposition](https://invisiblenetwork.ai/learn/nptel/111106160/b755c8354428) (Video)
38. [Fredholm Alternative Theorem](https://invisiblenetwork.ai/learn/nptel/111106160/bf8384148541) (Video)
39. [Orthogonal decomposition of self-adjoint operators](https://invisiblenetwork.ai/learn/nptel/111106160/9b4e0c378de5) (Video)
40. [Spectral family; Properties-I](https://invisiblenetwork.ai/learn/nptel/111106160/e8520f4693a0) (Video)
41. [Lecture 5: Spectral family; Properties-II](https://invisiblenetwork.ai/learn/nptel/111106160/770b3153f6be) (Video)
42. [Spectral theorem Self adjoint Operators](https://invisiblenetwork.ai/learn/nptel/111106160/38a1a38ce91a) (Video)
43. [Spectral theorem Examples](https://invisiblenetwork.ai/learn/nptel/111106160/4df7cabe74d4) (Video)
44. [Spectral theorem: Consequences](https://invisiblenetwork.ai/learn/nptel/111106160/5641bfb0c976) (Video)
45. [Continuous functional Calculus](https://invisiblenetwork.ai/learn/nptel/111106160/353587638aab) (Video)
46. [Spectral mapping theorem](https://invisiblenetwork.ai/learn/nptel/111106160/cf337a67b899) (Video)