News
06.04.2021

Teams LinkHere is a link to the Team "Funktionalanalysis 2b". 
31.03.2021

NewsSadly, Prof. Eschmeier passed away recently.
The Functional Analysis 2 lecture in the summer term is split into two parts: Sadly, Prof. Eschmeier passed away recently.
The Functional Analysis 2 lecture in the summer term is split into two parts: 
Functional analysis 2b (Operator algebras)
Lecture
Thursday, 1012, Team "Functional analysis 2b (Operator algebras)"
The language of the course is English, by default, unless all participants speak German.
In this lecture, which is formally a continuation of the lecture Functional Analysis (Funktionalanalysis), we will focus on the operator algebraic aspects of functional analysis. Operator algebras are generalizations of matrix algebras to the infinite dimensional setting; they are given as subalgebras of the algebra of all bounded linear operators on some Hilbert space that are invariant under taking adjoints and closed with respect to some specific topology. Roughly speaking, operator algebras are used to study by algebraic means the analytic properties of several operators simultaneously; their theory thus combines in a fascinating way linear algebra and analysis. The most prominent examples of such operator algebras are C*algebras and von Neumann algebras, which show a very rich structure and have various applications both in mathematics and physics, especially in quantum mechanics. Whereas the former have a more topological flavour (and their theory is thus often addressed as noncommutative topology), the latter has more measure theoretic and probabilistic sides and gives rise to noncommutative measure theory and noncommutative probability theory. We give an introduction to the theory of C*algebras covering amongst others the GNS construction, representation theory, and universal C*algebras. We might briefly mention von Neumann algebras in the end (such as factors and their classification, the hyperfinite factor, and group factors). 
Script
We will follow closely Chapters 17 of the following script:
ISem24 Lecture Notes
Exercises
The exercise sessions will be held by Marcel Scherer on Fridays, 1012 via Teams.
How to obtain the credit points
In order to obtain the credit points for this course, you must actively take part at the exercise sessions
(not missing them more than twice) and obtain 50% of the total of all points on the exercise sheets.
You will then be permitted to take part at the oral exams at the end of the term which are the basis
for your grade.
References
Books on operator algebras/C*algebras:
 Bruce Blackadar, Operator algebras. Theory of C*algebras and von Neumann algebras, 2006.
 Kenneth Davidson, C*algebras by example, 1996.
 Jacques Dixmier, Les C*algebres et leurs representations, 1969.
 Richard V. Kadison and John R. Ringrose, Fundamentals of the Theory of Operator Algebras.
Volume IIV, 1997.  Gerard Murphy, C*algebras and operator theory, 1990.
 Masamichi Takesaki, Theory of Operator Algebras IIII, 2002/2003
Books and lecture notes on von Neumann algebras:
 Claire Anantharaman and Sorin Popa, An introduction to II_{1} factors, preliminary version.
 Script by Vaughan Jones, Berkeley, 2009.
 Lecture Notes Von Neumann algebras and ergodic theory of group actions, IHP 2011.
 Script by Jesse Petersen, Vanderbilt, 2013.
 Script by Sven Raum, Münster, 2015/2016.
 Lecture Notes Von Neumann Algebras, Subfactors, Knots and Braids, and Planar Algebras
by Roland Speicher, Saarbrücken, 2016.  Lecture Notes by Cyril Houdayer, Paris