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Operators on normed spaces

Code: 61565
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Damir Bakić - Lectures
Lecturers: doc. dr. sc. Tomislav Berić - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: Basic properties of bounded operators on normed spaces


COURSE DESCRIPTION AND SYLLABUS:
1. Bounded operators.
2. Countinuous sesquilinear functionals on Hilbert spaces. The adjoint of a Hilbert space operator. Projections, unitary operators, partial isometries.
3. Uniform boundedness principle and its consequences.
4. Weak topologies.
5. Open mapping theorem and closed graph theorem.
6. Normed algebras. Spectrum and spectral radius.
7. Spectrum of a bounded operator. Properties.
8. Compact operators.
9. Spectral theorem for normal compact operators on Hilbert spaces.
Literature:
  1. S. Kurepa: Funkcionalna analiza
  2. G. Bachman, L. Narici: Functional analysis
  3. P. R. Halmos: A Hilbert space problem book
  4. G. K. Pedersen: Analysis NOW
Prerequisit for:
Enrollment :
Passed : Normed spaces
3. semester
Analiza - Regular study - Mathematics Education

4. semester
Analiza - Regular study - Mathematics Education
Consultations schedule:

Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/onp/

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/onnp_c