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master's thesis
C*-algebre kompaktnih operatora
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:979432
Junaković, Luka
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Junaković, L. (2022). C*-algebre kompaktnih operatora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:979432

Junaković, Luka. "C*-algebre kompaktnih operatora." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:979432

Junaković, Luka. "C*-algebre kompaktnih operatora." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:979432

Junaković, L. (2022). 'C*-algebre kompaktnih operatora', Master's thesis, University of Zagreb, Faculty of Science, accessed 11 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:979432

Junaković L. C*-algebre kompaktnih operatora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2025 January 11] Available at: https://urn.nsk.hr/urn:nbn:hr:217:979432

L. Junaković, "C*-algebre kompaktnih operatora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:979432

Metadata
TitleC*-algebre kompaktnih operatora
Title (english)C*-algebras of compact operators
AuthorLuka Junaković
MentorIlja Gogić (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-12-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog rada bio je prezentirati osnovnu teoriju C*-algebri s naglaskom na C*- algebre kompaktnih operatora. Nakon što se obrade glavni rezultati teorije Banachovih algebri, započinjemo s promatranjem jedne posebne klase Banachovih algebri, tzv. C*-algebri koje su po definiciji Banachove *-algebre čiji svaki element zadovoljava ||a*a|| = \(||a||^2\). Dokazan je Komutativni Gelfand-Naimarkov teorem koji ukratko kaže da svaku komutativnu C*-algebru možemo realizirati kao algebru neprekidnih funkcija na nekom lokalno kompaktnom Hausdorffovom prostoru koje iščezavaju u beskonačnosti. Nakon toga se razvija teorija reprezentacija C*-algebri što kulminira poznatim (nekomutativnim) Gelfand-Naimark teoremom koji kaže da se svaka C*-algebra može realizirati kao zatvorena, samoadjunigrana podalgebra algebre ograničenih operatora na nekom Hilbertovom prostoru. Nakon toga, naglasak je stavljen na analizu C*-algebri kompaktnih operatora, gdje u potpunosti opisujemo reprezentacije C*-algebri kompaktnih operatora te pomoću tog opisa dolazimo do njihovog strukturnog teorema.
Abstract (english)
The goal of this thesis was to present the basic theory of C*-algebras with emphasis on C*-algebras of compact operators. After the main results in the theory of Banach algebras are covered, we proceed with the study of so called C*-algebras, which are defined as complete *-algebras whose every element satisfies ||a*a|| = |\(||a||^2\). Commutative Gelfand-Naimark theorem is proven which, in short, states that every commutative C*-algebra can be realized as an algebra of continuous functions on some locally compact Hausdorff space which vanish at infinity. Next, we begin with the development of the representation theory of C*-algebras which culminates with the famous (noncommutative) Gelfand-Naimark theorem which states that every C*-algebra can be realized as a closed, self-adjoint, subalgebra of algebra of bounded operators on some Hilbert space. After that, the emphasis is given to the study of C*-algebras of compact operators, where we completely describe the representations of C*-algebras of compact operators and thus we deduce their structural theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:979432
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-12-16 12:08:11