by Law Yin King. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-64). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.5 / Chapter 1.1 --- The Enveloping von Neumann Algebra and Heredi- tary C*-Subalgebras --- p.5 / Chapter 1.2 --- C*-Crossed Products --- p.9 / Chapter 2 --- Hereditary C*-Subalgebras --- p.14 / Chapter 2.1 --- Polar Decompositions of Bounded Linear Functionals --- p.14 / Chapter 2.2 --- Unique State Extension --- p.19 / Chapter 2.3 --- Two Special Classes of Hereditary C*-Subalgebras --- p.25 / Chapter 3 --- C*-Crossed Products --- p.32 / Chapter 3.1 --- Hereditary C*-Subalgebras and Positive Definite Func- tions --- p.32 / Chapter 3.2 --- The Two Special Classes of Hereditary C*-Subalgebras in C*-Crossed Products --- p.43 / Chapter 3.3 --- Weak Expectations --- p.50 / Bibliography --- p.63

Pak Keung, Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 43). / Abstracts in English and Chinese. / Chapter 1 --- Preliminaries --- p.6 / Chapter 1.1 --- Definitions --- p.7 / Chapter 1.2 --- Topological Properties of the Structure Spaces of C*- Algebras --- p.14 / Chapter 1.3 --- "Topological Relations Between P(A), A and Prim(A)" --- p.17 / Chapter 2 --- Topological Properties of the Primal Ideal Spaces of C* - Algebras --- p.18 / Chapter 2.1 --- Topologies on Id(A) --- p.19 / Chapter 2.2 --- Minimal Primal Ideals and Their Topology --- p.31 / Chapter 3 --- Topological Representation of C*-Algebras --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Main Results --- p.39 / Bibliography --- p.43

Anderson and Putnam, and Kellendonk discovered methods of defining a C*- algebra on a noncommutative space associated with a tiling. The method employed was to use Renault's theory of groupoid C*-algebras of an equivalence relation on the tiling metric space. C*-algebras of a tiling have two purposes, on one hand they reveal information about the long range order of the tiling and on the other hand they provide interesting examples of C*-algebras. However, the two constructions do not include tilings such as the pinwheel tiling, with tiles appearing in an infinite number of orientations. We rectify this deficiency, with many interesting results appearing in the process.

by Ng Yin Fun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-51). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.4 / Chapter 1.1 --- Hilbert C*-modules --- p.4 / Chapter 2 --- Self-dual Hilbert C*-modules --- p.14 / Chapter 2.1 --- Self-duality --- p.14 / Chapter 2.2 --- Self-duality and some related concepts --- p.22 / Chapter 2.3 --- A criterion of self-duality of HA --- p.23 / Chapter 3 --- Hilbert W*-modules --- p.25 / Chapter 3.1 --- Extension of the inner product to --- p.25 / Chapter 3.2 --- Extension of operators to --- p.33 / Chapter 3.3 --- Self-dual Hilbert W*-modules --- p.36 / Chapter 3.4 --- Some equivalent conditions for a Hilbert W*-module to be self-dual --- p.43 / Bibliography --- p.50

by Lam Shek Ki. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 59-60). / Abstract also in Chinese. / Acknowledgment --- p.i / Abstract --- p.ii / Introduction --- p.2 / Chapter Chapter 1 --- Prelimnaries / Chapter §1.1 --- A Summary on C*-algebras and their representation theory --- p.4 / Chapter §1.2 --- Primitive ideals --- p.7 / Chapter §1.3 --- Canonical form of a matrix --- p.12 / Chapter Chapter 2 --- Uniqueness and basic properties of OA / Chapter §2.1 --- Uniqueness of Cuntz-Krieger Algebra --- p.13 / Chapter §2.2 --- Basic properties of OA --- p.25 / Chapter Chapter 3 --- A generalization of OA / Chapter §3.1 --- Universal Cuntz-Krieger Algebras --- p.33 / Chapter §3.2 --- Gauge action on AO A --- p.36 / Chapter Chapter 4 --- The ideal structure of OA and AO A / Chapter §4.1 --- Gauge-invariant ideals of AO A --- p.39 / Chapter §4.2 --- The primitive ideal space of AO A --- p.49 / Bibliography --- p.59

by Wong Wah Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 53-54). / Introduction --- p.2 / Chapter 1 --- Preliminaries --- p.3 / Chapter 1.1 --- A Summary on C*-algebras --- p.3 / Chapter 1.2 --- Hereditary C*-subalgebras --- p.5 / Chapter 1.3 --- C*-Inductive Limit --- p.7 / Chapter 1.4 --- Basic K-Theory of C*-algebras --- p.9 / Chapter 2 --- C*-algebras of Real Rank Zero --- p.14 / Chapter 2.1 --- Basic Properties of C*-algebras with Real Rank Zero --- p.14 / Chapter 2.2 --- Strongly Morita Equivalence and Extensions --- p.30 / Chapter 3 --- Simple C*-algebras --- p.42 / Chapter 3.1 --- Basic Properties --- p.42 / Chapter 3.2 --- Cuntz Algebras --- p.51 / Bibliography --- p.53

by Chau Man Pan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 74-75). / Abstracts in English and Chinese. / Chapter 1 --- Preliminaries --- p.6 / Chapter 1.1 --- General Theory of C* algebras --- p.6 / Chapter 1.2 --- Hilbert Modules and Induced representations --- p.11 / Chapter 1.3 --- Crossed Products --- p.15 / Chapter 2 --- Twisted crossed products --- p.18 / Chapter 2.1 --- Basic definition --- p.18 / Chapter 2.2 --- Iterated twisted crossed products --- p.24 / Chapter 3 --- Induced representations --- p.27 / Chapter 3.1 --- Construction of Imprimitivity bimodule --- p.27 / Chapter 3.2 --- Basic theory about induced representations --- p.32 / Chapter 4 --- Ideal Theory --- p.38 / Chapter 4.1 --- Induction and Restriction processes --- p.38 / Chapter 4.2 --- Sub-quotients of twisted crossed products --- p.48 / Chapter 5 --- Mackey Machine --- p.53 / Chapter 5.1 --- Quasi regular systems --- p.53 / Chapter 5.2 --- First Step of Mackey Machine --- p.57 / Chapter 5.3 --- Second step of Mackey Machine --- p.59 / Chapter 6 --- Abelian systems --- p.64 / Chapter 6.1 --- Dual spaces of Abelian systems --- p.64 / Chapter 7 --- Appendix --- p.69 / Chapter 7.1 --- Classical version of induced representation --- p.69

Chan, Wai-Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 52-53). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iii / Introduction --- p.iv / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- C*-algebras --- p.1 / Chapter 1.2 --- Topological groups --- p.8 / Chapter 2 --- Property T for topological groups --- p.18 / Chapter 2.1 --- Definitions and some basic properties --- p.18 / Chapter 2.2 --- Hereditary properties --- p.23 / Chapter 2.3 --- A characterization for property T --- p.26 / Chapter 2.4 --- Examples --- p.32 / Chapter 3 --- Property T for C*-algebras --- p.34 / Chapter 3.1 --- Countable discrete groups and their group C*- algebras --- p.34 / Chapter 3.2 --- Property T and nuclearity --- p.46 / Bibliography --- p.52

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 62-63). Also available for download via the World Wide Web; free to University of Oregon users.

Basic properties of pure functionals of a <I>C</I>^*-algebra are reviewed, and this is followed by an investigation of equivalent representations of a pure functional, restriction to ideals, and extension to bigger <I>C</I>^*-algebras. The relationship between notions of regularity for points in the spectrum of a <I>C</I>^*-algebra is studied. A localised version of Fell-Dixmier conditions for continuous trace of a <I>C</I>^*-algebra is obtained. The weak^*-closure of the space of pure functionals of arbitrary and homogeneous <I>C</I>^*-algebras is investigated. An analogue of Glimm's Vector State Space Theorem is proved. It is shown that G(A) = A^*₁ if and only if <I>A</I> is prime and antiliminal. Some results about the limits of pure functionals of an arbitrary <I>C^*-</I>algebra are obtained.