Michael Hartz

Functional Analysis 2

(Summer term 2020)


Time and Place

Tuesday, 14-16, online
Thursday, 14-16, online

Lectures will be held using Zoom, for which participants have received an invitation by email. The invitation can also be found on Moodle.

Exercise session: To be determined.

Office Hour: Thursday, after class, or by appointment


All material, including course notes, assignments and assignment solutions will be distributed using Moodle. To self-enrol for this course in Moodle, you need the enrolment key, which will be provided after registration by email. You are encouraged to use the discussion boards in Moodle for questions and discussion, both about general organization and about mathematics.


This course will be a continuation of Functional Analysis 1, taught by Prof. Groves during the winter term 2019/2020. Functional Analysis 2 will be divided into two parts, local convexity and operator algebras.

Locally convex spaces allow the study of notions of convergence that are not given by a norm, such as pointwise convergence of functions. They are also a convenient framework for the discussion of the important notions of weak and weak-* convergence.

The second part is concerend with the study of algebras of operators on Hilbert space. On the one hand, studying such algebras leads to insights into the structure of single operators. On the other hand, operator algebras are a fascinating topic in their own right, which has implications to group theory and mathematical physics.

List of topics:

Part I: Part II: Prerequisites are Functional Analysis 1.

Course Announcement


There will be weekly assignments. You are expected to achieve at least half of the available points on the assignments. At the end of the term, there will be an oral exam.


Part I:
Conway, John B., A course in functional analysis, 1990.
Lax, Peter D., Functional analysis, 2002.
Pedersen, Gert K., Analysis now, 1989.
Rudin, Walter, Functional analysis, 1991.
Werner, Dirk, Funktionalanalysis, 2000.

Part II:
Blackadar, Bruce, Operator algebras, 2006.
Davidson, Kenneth R., C*-algebras by example, 1996.
Dixmier, Jacques, C*-algebras, 1977.
Murphy, Gerard J., C*-algebras and operator theory, 1990.
Kadison, Richard V. and Ringrose, John R., Fundamentals of the theory of operator algebras. Vol. I, 1983.

Last update: May 07, 2020   Michael Hartz