Operators on normed spaces

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Code:	45657
ECTS:	5.0
Lecturers in charge:	izv. prof. dr. sc. Ilja Gogić
Lecturers:	izv. prof. dr. sc. Ilja Gogić - 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 type Total

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:

Prerequisit for:

Enrollment :
Attended : Normed spaces

Examination :
Passed : Normed spaces

2. semester

Mandatory course - Regular study - Applied Mathematics

Consultations schedule:

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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_a

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Operators on normed spaces

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