Department Mathematik



Exercises in
Functional Analysis II, winter 2014/15

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


20.01.2014 Please read the recent post about the exam and sign up (deadline: Jan 28).
05.11.2014 The exam will take place on February 5th between 9:00 and 12:00.
07.10.2014 The first exercise class will be on Oct 16.

Exercise class

The exercise class will take place each Thursday from 12 to 14 in B 041. There we will discuss the homework assignment released on the previous Thursday.

Exercise sheets

Last updated
Main topics
Thu, Oct 9
Assignment 1
Oct 14 (P2)
Compact operators, multiplication operators
Thu, Oct 16
Thu, Oct 16
Assignment 2
Oct 21 (P8)
Orthogonal projections, spectrum, resolvent
Thu, Oct 23
Thu, Oct 23
Assignment 3
Oct 23
Projections on Banach spaces, injectivity and compactness, spectra
Thu, Oct 30
Thu, Oct 30
Assignment 4
Oct 30
More spectra, Weyl sequences, multiplication operators
Thu, Nov 6
Thu, Nov 6
Assignment 5
Nov 11 (P18:c_n)
Square root, perturbation by compacts, Volterra integral operator
Thu, Nov 13
Thu, Nov 13
Assignment 6
Nov 17
Integral operators, spectral radius, absolute value of compacts, isometries
Thu, Nov 20
Thu, Nov 20
Assignment 7
Nov 25 (P26: H complex, P27i))
Weyl sequences II, Min-Max,
Volterra integral operator II
Thu, Nov 27
Thu, Nov 27
Assignment 8
Nov 27
Operator inequalities, decompositions,
normal operators
Thu, Dec 04
Thu, Dec 04
Assignment 9
Dec 04
Functional calculus, Stone's formula,
Discrete Laplacian
Thu, Dec 11
Thu, Dec 11
Assignment 10
Dec 16 (P38(ii):Hint)
Functional calculus, operator monotone functions, position operator
Thu, Dec 18
Thu, Dec 18
Assignment 11
Dec 18
Operator convex functions, one-parameter unitary group, cyclic vectors
Thu, Jan 08
Thu, Jan 08
Assignment 12
Jan 08
Cyclic vectors, unbounded mult. operators, adjoints, von Neumann
Thu, Jan 15
Thu, Jan 15
Assignment 13
Jan 15
Adjoints, closed operators, commutator, self-adjoint extensions
Thu, Jan 22
Thu, Jan 23
Assignment 14
Jan 23
Ess. s.a. operators, Dirichlet and Neumann Laplacian, Stone's theorem
Thu, Jan 29