Functional Analysis II
WS 2026/27
Docent: Tanja Eisner
Lectures:
Tuesday 15:15-16:45, 17:15-18:45 in SG 3-13
Exercises: Wednesday 09:15-10:45 in P-801
Requirement: Functional Analysis I
Description
The main topics of this course are
introduction to spectral theory (general properties of spectrum and resolvent, classification of spectrum, spectrum of isometries, unitaries and self-adjoint operators, Riesz' spectral theory of compact operators, Dunford's functional calculus);
weak and weak* topologies (theorems of Banach-Alaoglu and Krein-Milman);
spectral theorem for normal operators (multiplicator form).
If time allows, we will cover further classical topics from functional analysis and operator theory.
We will use in particular (but not exclusively) the following literature.
- D. Werner, "Funktionalanalysis", 3. edition, Springer-Verlag, Berlin, 2000.
- J. Conway, "A course in functional analysis", 2. edition, Springer-Verlag, New York, 1990.
- N. Dunford, J. Schwartz, "Linear Operators. Part I. General Theory", John Wiley & Sons, Inc., New York, 1988.
- K. Yosida, "Functional analysis", Springer-Verlag, Berlin, 1995.
- M. Reed, B. Simon, "Methods of modern mathematical physics. I. Functional
analysis." Second edition. Academic Press, New York, 1980.
- V. Kadets,
"A course in functional analysis and measure theory",
Springer, 2018.
- T. Eisner, B. Farkas, "A Journey Through Ergodic Theorems", Birkhäuser Verlag, 2025.
Notes
13.-20.10., 27.10.
Exercise Sheets
Sheet 1, Sheet 2, Sheet 3
Stefan Banach
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David Hilbert
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Frigyes Riesz
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Ivar Fredholm
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John von Neumann
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