| dc.rights.license | CC-BY-NC-ND | |
| dc.contributor.advisor | Ban, Prof. Dr. E.P. van den | |
| dc.contributor.author | Verstraten, R.C. | |
| dc.date.accessioned | 2017-08-23T17:01:46Z | |
| dc.date.available | 2017-08-23T17:01:46Z | |
| dc.date.issued | 2017 | |
| dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/26989 | |
| dc.description.abstract | We 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.sponsorship | Utrecht University | |
| dc.format.extent | 470891 | |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | |
| dc.title | The Gelfand-Naimark theorem for commutative Banach star algebras | |
| dc.type.content | Bachelor Thesis | |
| dc.rights.accessrights | Open Access | |
| dc.subject.keywords | Gelfand, Naimark, algebra, C*-algebra, functional calculus, Riesz functional calculus, spectral measures, representations, spectral theorem | |
| dc.subject.courseuu | Wiskunde | |
