Functional Analysis

This course consists of lectures and exercise classes (see timetable).

We will use the book by Bryan P. Rynne and Martin A. Youngson, 'Linear Functional Analysis', 2nd Edition, Springer.

Additional material: A really simple elementary proof of the uniform boundedness theorem

Each week there will be one or more excercises that will be graded. They can be made in (fixed) groups of two, and have to be handed in either at the next lecture (preferably in latex) or by email (in latex).

Exercises can be found here (version April 21, 2020).

With T being the grade for exam, and W de average of the homework grades without the lowest two, the final grade will be given by the usual rounding of T*7.5/10+max(T,W)*2.5/10, under the condition that T>= 5.

In case of a re-take, the final grade is given by the grade of that exam.

Lectures

week 6: Ch. 1, Ch. 2 until Thm. 2.26.
week 7: rest Ch. 2, Ch. 3 until Subsection 3.4
week 8: rest Ch. 3
week 9: Ch. 4 until Thm. 4.43
week 10: rest Ch. 4, Ch. 5 until Thm. 5.2
week 11: Ch. 5 until Sect. 5.3.
week 12: Ch. 5 up to and including the proof of Thm 5.13 on p138-139. The remainder of Sect. 5.4 is skipped. See here for notes on this week's material.
week 13: no lecture
week 14: Ch. 5 until Thm. 5.50. Lecture notes.
week 15: rest Sect. 5 (without Lemma 5.67 (and all further references to this metric), Lemma 5.70(d), and Corollary 5.74) until Thm 5.71. Lecture notes.
week 16: Thm 5.73. Ch. 6 until Thm. 6.39. Lecture notes.
week 17: rest Ch. 6. Lecture notes.
week 18: Sect 7.1. Lecture notes.
week 20: Sect 7.2. Lecture notes.
week 22: Exam. The material from Rynne and Youngson as indicated above.
week 27: re-take.

Exercise classes

(hand-in exercises in bold (will be indicated after class))

week 6: 1, 2, 3, 4, 5, 6.
week 7: 2.10, 2.11, 2.12, 3.16, 3.19. 7, 8, 9, 10.
week 8: 3.22, 3.24, 3.25, 3.26, 11, 12, 13, 43
week 9: 2.14, 4.13, 4.19 (replace the given condition on the norm of the inverses being smaller than 1 by uniform boundedness of these norms), 14, 15, 16a,b, 16c, 17.
week 10: 18, 19, 20, 21, 5.2.
week 11: 5.1, 5.3, 5.4, 5.5, 23, 24
week 12: 5.7, 5.8, 22, 25, 28
week 13: 1, 2, 3, 4, and 5 from midterm + solutions.
week 14: 5.15, 5.16, 5.20, 30, 27
week 15: 31, 5.17, 5.18, 32, 5.25, 33
week 16: 6.8, 6.14, 34, 35a,b,c,d(i),35d(ii), 36, 37, 38 week 17: 39 a,b, 39 c,d,e, 40, 6.18, 6.22, 6.30.
week 18: 42, 7.8, 7.11 (Erratum 7.11c), 7.13, 7.14.
week 19: Training material: Midterm last year + solutions. Re-take last year."
week 20: 7.18, 7.20, 7.21, 41