Thesis (M.Sc.)(Mathematics)--University of Pretoria, 2004. / Title from opening screen (viewed March 11th, 2005). Includes summary. Includes bibliographical references.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-graduação em Matemática e Computação Científica / Made available in DSpace on 2012-10-23T09:44:39Z (GMT). No. of bitstreams: 1 241325.pdf: 738620 bytes, checksum: 159a6b746e21d7f151d91859e6cb3a5a (MD5) / Sejam H um espaço de Hilbert separável e S1, S2 em B(H) duas isometrias. Dizemos que S1 e S2 são compatíveis se S1 comuta com S2 e, para quaisquer m,n em N, temos que S1^{m}(S1*)^{m} comuta com S2^{n}(S2*)^{n}, isto é, as projeções finais de S1^{m} e S2^{n} comutam. Nosso principal objetivo neste trabalho é caracterizar a C*-álgebra gerada por duas isometrias compatíveis como um produto cruzado parcial. Para isto, desenvolveremos a teoria de ações parciais, representações parciais e produtos cruzados parciais. Além disso, no capítulo final construiremos uma classe de representações desta C*-álgebra fazendo uso da teoria de representações induzidas.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Matemática Pura e Aplicada, Florianópolis, 2014. / Made available in DSpace on 2014-08-06T18:02:24Z (GMT). No. of bitstreams: 1 327232.pdf: 596083 bytes, checksum: 1095fb8896d9cdc111e05c1e419e6e2c (MD5) Previous issue date: 2014 / Neste trabalho estudamos as K-teorias algébrica, topológica e de C-álgebras.Mostramos que se A é uma C-álgebra unital, então K0(A) é o mesmo (a menos de isomorfismo) na K-teoria algébrica e na K-teoria de C-álgebras. Além disso, considerando X um espaço topológico compacto Hausdorff, provamos o Teorema de Serre-Swan, isto é, que existe uma equivalência categórica entre a categoria dos C(X)-módulos projetivos finitamente gerados e a categoria dos fibrados vetoriais sobre X.<br> / Abstract : In this work we study algebraic and topological K-theory and the K-theory of C-algebras. We show that if A is a unital C-algebra then K0(A) is (up to isomorphism) the same in algebraic K-theory and in the K-Theory of C-Algebras. More over, we show the Serre-Swan theorem, which says that if Xis a compact Hausdorff space then there is a categorical equivalence between the category of finitely generated projective C(X)-modules and the category of vector bundles over X.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Matemática Pura e Aplicada, Florianópolis, 2016. / Made available in DSpace on 2017-01-31T03:08:44Z (GMT). No. of bitstreams: 1 343945.pdf: 549756 bytes, checksum: 06e4eb8385f32b7c09ecbca723f8ae81 (MD5) Previous issue date: 2016 / Neste trabalho, estudaremos semigrupos inversos e algumas álgebras associadas a estes objetos. Mais precisamente, serão estudados os semigrupos inversos E-unitários. Veremos que todo semigrupo inverso E-unitário S pode ser descrito como um produto semidireto de E, o semirreticulado dos idempotentes de S, por G, o grupo imagem homomorfa máxima de S, via uma ação parcial proveniente de uma ação deste semigrupo sobre E. Em seguida, será definida a C*-álgebra de semigrupos inversos e estudados produtos cruzados parciais. O principal resultado mostra que se S é um semigrupo inverso E-unitário, então C*(S) é canonicamente isomorfa a C0(Ê)?G. Daremos algumas aplicações para este resultado e, em particular, descreveremos a C*-álgebra do semigrupo inverso universal de Exel como um produto cruzado parcial.<br> / Abstract : In this work we study inverse semigroups and some algebras associated to them. More precisely, we shall study E-unitary inverse semigroups. We shall see that every E-unitary inverse semigroup S can be described as a semidirect product of E, the semilattice of idempotents of S by the maximal group homomorphic image of S via a partial action of this group that is induced from the canonical action of S on E. We shall define and study C*-algebras of inverse semigroups and partial crossed products. The main result shows that C*(S) is canonically isomorphic C0(Ê) ? G if S is E-unitary and G is the maximal group homomorphic image of S. We give some applications of this result and, in particular, describe Exel's universal inverse semigroup C*-algebra as a partial crossed product.

En este trabajo examinamos los C*-algebras de operadores Toeplitz sobre la bola unitaria en Cn y en el polidisco unitario en C². Los operadores Toeplitz son ejemplos interesantes de operadores que no son operadores normales y que generan C*-algebras no conmutativas. Además, en los mejores casos de álgebras de operadores Toeplitz (dependiendo de la geometría del dominio) podemos recuperar algunos resultados análogos al teorema espectral módulo operadores compactos. En este contexto, podemos capturar el índice de un operador Fredholm que es un invariante numérico fundamental en Teoría de Operadores / In this work we examine C*-algebras of Toeplitz operators over the unit ball inCn and the unit polydisc in C². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the domain) of algebras of Toeplitz operators we can recover some analogues of the spectral theorem up to compact operators. In this setting, we can capture the index of a Fredholm operator which is a fundamental numerical invariant in Operator Theory.

Given a C*-algebra $\\A$, an irredundant set in $\\A$ is a subset $\\mathcal$ of $\\A$ such that no $a\\in \\mathcal$ belongs to the C*-subalgebra generated by $\\mathcal\\setminus\\{a\\}$. Every separable C*-algebra has only countable irredundant sets and we ask if every nonseparable C*-algebra has an uncountable irredundant set. For commutative C*-algebras, if $K$ is the Kunen line then $C(K)$ is a consistent example of a nonseparable commutative C*-algebra without uncountable irredundant sets. On the other hand, a result due to S. Todorcevic establishes that it is consistent with ZFC that every nonseparable C*-algebra of the form $C(K)$, for a compact 0-dimensional space $K$, has an uncountable irredundant set. By the method of forcing, we construct a nonseparable and noncommutative scattered C*-algebra $\\A$ without uncountable irredundant sets and with no nonseparable abelian subalgebras. On the other hand, we prove that it is consistent that every C*-subalgebra of $\\B(\\ell_2)$ of density continuum has an irredundant set of size continuum. / Given a C*-algebra $\\A$, an irredundant set in $\\A$ is a subset $\\mathcal$ of $\\A$ such that no $a\\in \\mathcal$ belongs to the C*-subalgebra generated by $\\mathcal\\setminus\\{a\\}$. Every separable C*-algebra has only countable irredundant sets and we ask if every nonseparable C*-algebra has an uncountable irredundant set. For commutative C*-algebras, if $K$ is the Kunen line then $C(K)$ is a consistent example of a nonseparable commutative C*-algebra without uncountable irredundant sets. On the other hand, a result due to S. Todorcevic establishes that it is consistent with ZFC that every nonseparable C*-algebra of the form $C(K)$, for a compact 0-dimensional space $K$, has an uncountable irredundant set. By the method of forcing, we construct a nonseparable and noncommutative scattered C*-algebra $\\A$ without uncountable irredundant sets and with no nonseparable abelian subalgebras. On the other hand, we prove that it is consistent that every C*-subalgebra of $\\B(\\ell_2)$ of density continuum has an irredundant set of size continuum.

by Leung Chi Wai. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaf [51]

A C*-algebra is called primitive if it admits a *-representation that is both faithful and irreducible. Thus the simplest examples are matrix algebras. The main objective of this work is to classify unital full free products of finite dimensional C*-algebras that are primitive. We prove that given two nontrivial finite dimensional C*-algebras, A1 /= C, A2 /= C, the unital C*-algebra full free product A = A1 * A2 is primitive except when A1 = C^2 = A2. Roughly speaking, we first show that, except for trivial cases and the case A1 = C^2 = A2, there is an abundance of irreducible finite dimensional *-representations of A. The latter is accomplished by taking advantage of the structure of Lie group of the unitary operators in a finite dimensional Hilbert space. Later, by means of a sequence of approximations and Kaplansky?s density theorem we construct an irreducible and faithful {representation of A. We want to emphasize the fact that unital full free products of C*-algebras are highly abstract objects hence finding an irreducible *-{representation that is faithfully is an amazing fact. The dissertation is divided as follows. Chapter I gives an introduction, basic definitions and examples. Chapter II recalls some facts about *-automorphisms of finite dimensional C -algebras. Chapter III is fully devoted to prove Theorem III.6 which is about perturbing a pair of proper unital C*-subalgebras of a matrix algebra in such a way that they have trivial intersection. Theorem III.6 is the cornerstone for the rest of the results in this work. Lastly, Chapter IV contains the proof of the main theorem about primitivity and some consequences.

Erratum (14 leaves) in pocket / Bibliography: leaves 124-128 / x, 128 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics,1986

Thesis (Ph.D.) -- University of Newcastle, 2003. / School of Mathematical and Physical Sciences. Includes bibliographical references (p. 161-162). "Also available online".