1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

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.

1. Funkcionalna analiza, S. Kurepa, Školska knjiga, Zagreb, 1981.
2. Functional analysis, G. Bachman, L. Narici, Academic Press, 1966.
3. A Hilbert space problem book, P. R. Halmos, Van Nostrand, 1967.
4. Analysis NOW, G. K. Pedersen, Springer Verlag, 1998.

Enrollment :
Attended : Normed spaces

Examination :
Passed : Normed spaces

Mandatory course - Regular study - Theoretical Mathematics