dc.contributor.advisor Farah, Ilijas dc.creator Ghasemi, Saeed dc.date.accessioned 2015-08-28T15:44:37Z dc.date.available 2015-08-28T15:44:37Z dc.date.copyright 2015-04-13 dc.date.issued 2015-08-28 dc.identifier.uri http://hdl.handle.net/10315/30112 dc.description.abstract In this thesis we use techniques from set theory and model theory to study the isomorphisms between certain classes of C*-algebras. In particular we look at the isomorphisms between corona algebras of the form $\prod\mathbb{M}_{k(n)}(\mathbb{C})/\bigoplus \mathbb{M}_{k(n)}(\mathbb{C})$ for sequences of natural numbers $\{k(n): n\in\mathbb{N}\}$. We will show that the question whether any isomorphism between these C*-algebras is trivial", is independent from the usual axioms of set theory (ZFC). We extend the classical Feferman-Vaught theorem to reduced products of metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent. We also use this to find examples of corona algebras of the form $\prod\mathbb{M}_{k(n)}(\mathbb{C}) / \bigoplus \mathbb{M}_{k(n)}(\mathbb{C})$ which are non-trivially isomorphic under the Continuum Hypothesis. This gives the first example of genuinely non-commutative structures with this property. In chapter 6 we show that $SAW^{*}$-algebras are not isomorphic to $\nu$-tensor products of two infinite dimensional C*-algebras, for any C*-norm $\nu$. This answers a question of S. Wassermann who asked whether the Calkin algebra has this property. dc.language.iso en dc.rights Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests. dc.subject Mathematics dc.subject Theoretical mathematics dc.title Rigidity of Corona Algebras dc.type Electronic Thesis or Dissertation en_US dc.degree.discipline Mathematics & Statistics dc.degree.name PhD - Doctor of Philosophy dc.degree.level Doctoral dc.date.updated 2015-08-28T15:44:37Z dc.subject.keywords Corona algebra dc.subject.keywords Rigidity dc.subject.keywords C*-algebra dc.subject.keywords Reduced products dc.subject.keywords FDD-algebras dc.subject.keywords Isomorphism dc.subject.keywords Automorphism dc.subject.keywords Metric Feferman-Vaught theorem dc.subject.keywords SAW*-algebras
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