Department Mathematik



Exercises in
Functional Analysis II, winter 2015/16

This site provides material for the exercise classes complementing the lecture course Functional Analysis 2 held by Prof. Thomas Østergaard Sørensen, PhD.


16.02.2016 This site is no longer updated.
10.02.2016 Reminder: Deadline for the registration to the oral re-exam is
Tuesday, February 16th, 12:00.
10.02.2016 The results of the exam are now posted at the door of room B403.
05.02.2016 There is updated information about the re-exam on the lecture website.
26.01.2016 Please read the notice about the exam on the lecture website and sign up.
Deadline: registration closed.

Exercise class

The exercise class will take place each Friday from 12 to 14 in A 027. There we will discuss the homework assignment released on the previous Friday.

Exercise sheets

Last updated
Main topics
Fri, Oct 16
Assignment 1
Compact operators, multiplication operators
Fri, Oct 23
Fri, Oct 23
Assignment 2
Orthogonal projections, spectrum, resolvent
Fri, Oct 30
Fri, Oct 30
Assignment 3
Projections on Banach spaces, injectivity and compactness, spectra
Fri, Nov 06
Fri, Nov 06
Assignment 4
More spectra, Weyl sequences, multiplication operators
Fri, Nov 13
Fri, Nov 13
Assignment 5
Square root, perturbation by compacts, Volterra integral operator
Fri, Nov 20
Fri, Nov 20
Assignment 6
Integral operators, spectral radius, absolute value of compacts, isometries
Fri, Nov 27
Fri, Nov 27
Assignment 7
Decompositions, Weyl sequences II,
Min-Max, Volterra integral operator II
Fri, Dec 04
Fri, Dec 04
Assignment 8
Dec 10, P32(iii)
Operator inequalities, commuting operators, normal operators
Fri, Dec 11
Fri, Dec 11
Assignment 9
Functional calculus, Stone's formula,
Discrete Laplacian
Fri, Dec 18
Thu, Dec 18
Assignment 10
Functional calculus, operator monotone functions, position operator
Fri, Jan 08
Wed, Dec 23
Holiday Extra
Jan 13 (cor. grammar)
Functional Calculus for commuting s.a. operators and normal operators
Fri, Jan 08
Assignment 11
Operator convex functions, one-par. unitary group, cyclic vectors
Fri, Jan 15
Fri, Jan 15
Assignment 12
Cyclic vectors, unbounded mult. operators, adjoints, von Neumann
Fri, Jan 22
Fri, Jan 22
Assignment 13
closed operators, commutation relation, self-adjoint extensions
Fri, Jan 29
Fri, Jan 29
Assignment 14
Ess. s.a. operators, Dirichlet and Neumann Laplacian, Stone's theorem
Fri, Feb 05