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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorBan, Prof. Dr. E.P. van den
dc.contributor.authorVerstraten, R.C.
dc.date.accessioned2017-08-23T17:01:46Z
dc.date.available2017-08-23T17:01:46Z
dc.date.issued2017
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/26989
dc.description.abstractWe start by studying properties of several kinds of algebras, taking a look at the spectrum, ideals and abelian algebras. Then we prove the Gelfand-Naimark Theorem for commutative Banach star algebras (also known as abelian C*-algebras). After that, we prove some basic theorems about Riemann integration of Banach valued functions. We then study some applications of the Gelfand-Naimark Theorem where we start by studying the functional calculus, in particular the Riesz functional calculus and its extension to C*-algebras. We then take a look at positive elements, representations of C*-algebras and in particular the Gelfand-Naimark-Segal construction. Lastly, we study spectral measures and, using representations, we prove the spectral theorem for bounded normal operators on a Hilbert space.
dc.description.sponsorshipUtrecht University
dc.format.extent470891
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.titleThe Gelfand-Naimark theorem for commutative Banach star algebras
dc.type.contentBachelor Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsGelfand, Naimark, algebra, C*-algebra, functional calculus, Riesz functional calculus, spectral measures, representations, spectral theorem
dc.subject.courseuuWiskunde


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