401-3461-00L  Functional Analysis I

SemesterAutumn Semester 2019
LecturersM. Struwe
Periodicityyearly recurring course
Language of instructionEnglish
CommentAt most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.


401-3461-00 VFunctional Analysis I4 hrs
Mon10:15-12:00HG D 7.1 »
Thu13:15-15:00HG G 5 »
M. Struwe
401-3461-00 UFunctional Analysis I
Groups are selected in myStudies.
1 hrs
Mon09:15-10:00HG E 21 »
09:15-10:00HG F 26.5 »
09:15-10:00HG G 26.1 »
09:15-10:00HG G 26.5 »
M. Struwe

Catalogue data

AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
LiteratureWe will be using the Lecture Notes on

"Funktionalanalysis I" by Michael Struwe.

Other useful, and recommended references include the following books:

Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011.

Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017.

Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Elias M. Stein and Rami Shakarchi: "Functional analysis" (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.

Dirk Werner, "Funktionalanalysis". Springer-Lehrbuch, 8. Auflage. Springer, 2018
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersM. Struwe
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 180 minutes
Written aidsA short collection of useful results will be provided by the lecturer.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Main linklecture homepage
LiteratureLecture notes
Only public learning materials are listed.


401-3461-00 UFunctional Analysis I
Mon09:15-10:00HG E 21 »
Mon09:15-10:00HG F 26.5 »
Mon09:15-10:00HG G 26.1 »
Mon09:15-10:00HG G 26.5 »


There are no additional restrictions for the registration.

Offered in

High-Energy Physics (Joint Master with EP Paris)Optional Subjects in MathematicsWInformation
Mathematics BachelorCore Courses: Pure MathematicsWInformation
Mathematics MasterBachelor Core Courses: Pure MathematicsE-Information
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Physics MasterSelection: MathematicsWInformation