Syllabus

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

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  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).

Description