O epimorfnoj slici centra C*-algebre

master's thesis

• Author: Mateo Tomašević
• Mentor: Ilja Gogić (mentor)
• Committee member: Ilja Gogić (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Neka su \(A\) i \(B\) unitalne \(C^*\)-algebre s centrima \(Z(A)\) i \(Z(B)\) i neka je \(\phi : A \to B\) \(*\)-epimorfizam. Tada svakako vrijedi \(\phi(Z(A)) \subseteq Z(B)\). U ovom diplomskom radu izlažemo Vesterstrømov teorem iz 1971. koji daje nužan i dovoljan uvjet na unitalnu \(C^*\)-algebru \(A\) takvu da za svaku \(C^*\)-algebru \(B\) i \(*\)-epimorfizam \(\phi : A \to B\) vrijedi jednakost \(\phi(Z(A)) = Z(B)\). Za dokaz ovog teorema uvodimo pojmove spektra \(C^*\)-algebre i prostora primitivnih ideala s pripadnim topologijama, te klase centralnih i slabo centralnih unitalnih \(C^*\)-algebri. Konačno, dajemo neke značajnije primjere \(C^*\)-algebri koje zadovoljavaju gornje svojstvo.

Abstract (english)

Let \(A\) and \(B\) be unital \(C^*\)-algebras with centers \(Z(A)\) and \(Z(B)\), and let \(\phi : A \to B\) be a \(*\)-epimorphism. Then we certainly have \(\phi(Z(A)) \subseteq Z(B)\). In this master thesis we present Vesterstrøm’s theorem from 1971 which provides necessary and sufficient conditions on a unital \(C^*\)-algebra \(A\) such that for every \(C^*\)-algebra \(B\) and \(*\)-epimorphism \(\phi : A \to B\) we have the equality \(\phi(Z(A)) = Z(B)\). To prove this theorem we introduce the spectrum of a \(C^*\)-algebra and the primitive ideal space equipped with respective topologies, along with two classes of \(C^*\)-algebras: central and weakly central. To finalize we give some notable examples of \(C^*\)-algebras satisfying the above property.

• Keywords: Vesterstrømov teorem; C* algebra
• Keywords (english): Vesterstrøm's teorem; C* algebra
• Language: croatian
• URN:NBN: urn:nbn:hr:217:166939
• Study programme: Title: Pure Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-06-25 11:17:03