Malenica, Ante (2015) C*algebre i njihove reprezentacije. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract
A Banach algebra supplied with an involution and a norm satisfying the condition $\ a ^\ast a \ = \a\^2$, for every element $\alpha$, is called a $C^\ast$algebra. The approach used in this thesis was to first introduce the main ideas and theorems of the theory of Banach algebras and then to move on to the theory $C^\ast$algebra and presented its important results. After proving the existence of Gelfand transformation of abelian Banach algebras, this result has been generalized to abelian $C^\ast$algebras, where the said mapping has been proved to be an isometric $\ast$isomophism. Additionally, we have shown a close relationship between closed left ideals and hereditary $C^\ast$subalgebras, and the latter are, in the case of separability of the original space, closely related to positive elements of the observed $C^\ast$algebra. Finally, we have presented a famous resut of Gelfand and Naimark stating the existence of a faithful representation of an arbitrary $C^\ast$algebra.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Bakić, Damir 
Date:  2015 
Number of Pages:  38 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  22 Oct 2015 09:35 
Last Modified:  22 Oct 2015 09:35 
URI:  http://digre.pmf.unizg.hr/id/eprint/4295 
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