20.500.12556/DKUM-93532 Omejeni linearni operatorji na Hilbertovih prostorih na študijskem programu 2. stopnje Matematika Bounded linear operators on Hilbert spaces magistrsko delo V magistrskem delu predstavimo in preučujemo omejene linearne operatorje na Hilbertovih prostorih. V prvem delu uvedemo osnovne pojme in dokažemo ali navedemo nekatere rezultate s področja funkcionalne analize, kot so Hahn-Banachov izrek, izrek o odprti preslikavi ter Rieszov izrek. V drugem delu nato uvedemo pojem adjungiranega operatorja in z njegovo pomočjo naredimo pregled raznih posebnih tipov omejenih linearnih operatorjev. Posebej obravnavamo normalne, sebi-adjungirane in unitarne operatorje ter ortogonalne projektorje na kompleksnih Hilbertovih prostorih. Na koncu definiramo spekter omejenega linearnega operatorja na kompleksnem Hilbertovem prostoru in dokažemo nekaj osnovnih rezultatov. Te nato uporabimo pri nadaljnjem študiju omejenih linearnih operatorjev ter pri definiciji in proučevanju pozitivnih operatorjev na kompleksnih Hilbertovih prostorih. In the thesis we define and study bounded linear operators on Hilbert spaces. In the first section we introduce some elementary concepts and prove or list some results from the field of functional analysis, such as the Hahn-Banach theorem, the open mapping theorem and the Riesz theorem. In the second section we then introduce the concept of an adjoint operator and use it to take a look at various special types of bounded linear operators. In particular, we study normal, self-adjoint and unitary operators as well as orthogonal projectors on complex Hilbert spaces. Finally, we define the concept of the spectrum of a bounded linear operator on a complex Hilbert space and prove some elementary results. We then use those results to continue studying bounded linear operators and to define and study positive operators on complex Hilbert spaces. Linearna algebra funkcionalna analiza Hilbertov prostor omejen linearen operator spekter spektralni radij normalen operator unitaren operator sebi-adjungiran operator. Linear algebra functional analysis Hilbert space bounded linear operator spectrum spectral radius normal operator unitary operator self-adjoint operator. true true false [J. Zakeršnik] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-07-01 11:49:33 2025-08-26 13:26:01 2025-08-27 03:50:20 0000-00-00 00:00:00 2025 0 Maribor 0 Maribor VIII, 69 f. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.983.24(043.2) 246663171 MAG_Zakersnik_Jimmy_2025.pdf MAG_Zakersnik_Jimmy_2025.pdf 1 FEE03B2C7657FA7BFCC9F21E5CE3FA96 7088659ddcad83e4a19a5a6b191b2927594559e12b8da239f2b3a7c41b9ccee6 34951ac9-566d-11f0-8520-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193052 Fakulteta za naravoslovje in matematiko 0 0 0