MAL6060: Functional Analysis (M. Sc. course) at IIT Jodhpur

Course plan: We will be learning Functional Analysis. 

Assignments, additional related material will be posted on this page. 

Course evaluation, policy details and dates: see here

Resources: For a brief historical account by Neal L. Carothers : see here. 

Lecture plan:

2nd Jan 2026 : Recall about Metric spaces, Examples of metrics d_p on K^n, inequalities by Young, Hölder and Minkowski

5th Jan : Lecture 1: Further examples of metric spaces: sequences spaces, function spaces

7th Jan : Lecture 2: Normed spaces, basic properties of normed spaces

9th Jan : Lecture 3: Subspaces of normed spaces, Quotients of normed spaces 

12th Jan : Lecture 4: Riesz' lemma, Finite dimensional subspaces of normed spaces are complete. 

14th Jan : Lecture 5:  Topological characterization of Finite dimesional normed spaces, Equivalence of norms

16th Jan : No class

19 th Jan : Lecture 6: Continuity of linear maps 

20st Jan : L7: Characterization of countinuous maps

21st Jan : L8: Bounded linear maps, norm of operator 

23rd Jan : L9: Hahn-Banach theorems   

26 Jan : Holiday 

28 jan: Tutorial session 

30 Jan: No class. Quiz 1 this week on Friday 30th Jan

2nd Feb: L10: Hahn-Banach theorems, Applications

 3rd Feb: L11:  Banach spaces, Examples, Summability 

4th Feb: L12:  Uniform boundedness principles

9th Feb : L13: Open map theorem 

11th Feb: L14:  Closed graph theorem

13th Feb: L15: Bounded linear functionals, dual spaces, 

16th Feb: L16: reflexive normed spaces

18-21 Feb: Minor exam period

23 Feb: L^p spaces

25 Feb:

27th Feb:

2nd March:

4th March : Holi Holiday

6th March:

9th March:

11th March: 

Semester break

18th March : Geometry of Hilbert spaces and applications

20th March

23rd March 

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1 April

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