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401-3461-00L 10 Credits BSC , MSC D-MATH , D-PHYS
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Functional Analysis I

Lecturers & Examiners: Dr. Alessandro Carlotto
At 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. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office ( ) after having received the credits.
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Last Updated: 2026-02-05 15:35:47

Abstract

Baire 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.

Objective

Acquire 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.

Resources

Literature

Recommended references include the following: Michael Struwe: "Funktionalanalysis I" (Skript available at https://people.math.ethz.ch/~struwe/Skripten/FA-I-2019.pdf ) Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011. 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. Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017. Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
none

Course Components

Type Title Time & Place Hours
lecture Functional Analysis I
Studierende besuchen die Lehrveranstaltung alternierend eine Woche in Präsenz, die folgende Woche online. Erste Unterrichtswoche Präsenz: Nachname beginnend mit «A» bis «L» Erste Unterrichtswoche Online: Nachname beginnend mit «M» bis «Z» danach alternierend. Ab November 2020: für alle online.
  • Mon 10:15-12:00 (HG G 5)
  • Thu 14:15-16:00 (HG G 5)
4 h weekly
exercise Functional Analysis I
Groups are selected in myStudies.
  • Mon 09:15-10:00 (CAB G 51)
  • Mon 09:15-10:00 (HG D 5.2)
  • Mon 09:15-10:00 (HG E 33.3)
  • Mon 09:15-10:00 (ML F 39)
1 h weekly

Offered In