Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


You will learn about norms and seminorms in infinite-dimensional vector spaces. Related to these structures, you will understand basic properties of bounded linear operators, duality and spectral theory in Banach spaces.

Credits: 5

Schedule: 27.10.2020 - 09.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Ville Turunen

Teacher in charge (applies in this implementation): Ville Turunen

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Bounded linear operators, compact linear operators, functionals, and elementary spectral theory in Banach spaces (Riesz Compactness Theorem, Zabreiko's Lemma, Uniform Boundedness Principle, Open Mapping and Closed Graph Theorems, Hahn-Banach Theorem, Gelfand's Spectral Theorem).

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Weekly exercises (1/3) and an exam (2/3). Alternatively, just exam (100%).

  • Valid 01.08.2020-31.07.2022:

    Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca 100h.


Study Material
  • Valid 01.08.2020-31.07.2022:

    Lecture notes (additional literature to be announced at the course homepage).

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Mat-1.3460 Principles of Functional Analysis.

  • Valid 01.08.2020-31.07.2022:

    MS-A00XX, MS-A01XX, MS-C1540


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