Please note! Course description is confirmed for two academic years, 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.

LEARNING OUTCOMES

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: 25.10.2022 - 07.12.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Ville Turunen, Topi Kuutela

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

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content
  • valid for whole curriculum period:

    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 for whole curriculum period:

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

Workload
  • valid for whole curriculum period:

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

DETAILS

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information
  • valid for whole curriculum period:

    Teaching Language : English

    Teaching Period : 2022-2023 Autumn II
    2023-2024 No teaching

    Enrollment :

    Registration takes place in Sisu (sisu.aalto.fi).