An exposition of Hilbert C-modules
- Authors: Sokopo, Bulelani Joab
- Date: 2015
- Subjects: Mathematics Algebra , Functions, Continuous Mathematical analysis
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/50008 , vital:41974
- Description: In trying to prove that derivations of type I AW -algebras are inner, I. Kaplansky introduced and developed the basics of the concept of Hilbert C- modules. He sought to generalize the idea of a Hilbert space by replacing the field C of all complex numbers with a general (commutative and unital) C-algebra. Twenty years later, the concept was broadened and expanded to non-commutative C-algebras by W. L. Paschke and M. A. Rieffel in their papers on inner product modules over B-algebras and induced representations of C-algebras, respectively. Since then, the theory of Hilbert C-modules has grown rapidly. It was used by G. G. Kasparov as the framework for his bivariant K-theory. More recently, Hilbert C-modules have formed the technical basis for the C*-algebraic approach to quantum group theory. The aim of this dissertation is to provide as detailed an account as possible of the theory of Hilbert C-modules, as given in a book of E. C. Lance, up to and including the KSGNS construction. The KSGNS construction, named after Kasparov, Stinespring, Gelfand, Naimark and Segal, is a generalization to Hilbert C-modules of the familiar GNS construction for C-algebras. The result by Kaplansky that all derivations of a type I AW-algebra are inner is given as an application in the final chapter of the dissertation.
- Full Text:
- Date Issued: 2015
- Authors: Sokopo, Bulelani Joab
- Date: 2015
- Subjects: Mathematics Algebra , Functions, Continuous Mathematical analysis
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/50008 , vital:41974
- Description: In trying to prove that derivations of type I AW -algebras are inner, I. Kaplansky introduced and developed the basics of the concept of Hilbert C- modules. He sought to generalize the idea of a Hilbert space by replacing the field C of all complex numbers with a general (commutative and unital) C-algebra. Twenty years later, the concept was broadened and expanded to non-commutative C-algebras by W. L. Paschke and M. A. Rieffel in their papers on inner product modules over B-algebras and induced representations of C-algebras, respectively. Since then, the theory of Hilbert C-modules has grown rapidly. It was used by G. G. Kasparov as the framework for his bivariant K-theory. More recently, Hilbert C-modules have formed the technical basis for the C*-algebraic approach to quantum group theory. The aim of this dissertation is to provide as detailed an account as possible of the theory of Hilbert C-modules, as given in a book of E. C. Lance, up to and including the KSGNS construction. The KSGNS construction, named after Kasparov, Stinespring, Gelfand, Naimark and Segal, is a generalization to Hilbert C-modules of the familiar GNS construction for C-algebras. The result by Kaplansky that all derivations of a type I AW-algebra are inner is given as an application in the final chapter of the dissertation.
- Full Text:
- Date Issued: 2015
Psychologists' perceived influences of early strategies on the psychosocial response to those affected by disasters
- Authors: Blackburn, Nerina June
- Date: 2010
- Subjects: Disasters -- Psychological aspects , Post-traumatic stress disorder , Disaster victims -- Mental health , Disasters
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9872 , http://hdl.handle.net/10948/1416 , Disasters -- Psychological aspects , Post-traumatic stress disorder , Disaster victims -- Mental health , Disasters
- Description: Currently some confusion exists as to how health professionals should best respond to the psychological needs of those affected by disasters. Some have argued that early psychological intervention is essential and others have argued that early formal psychological interventions have no useful role in post trauma response. This study highlights the importance of considering both counselling and non-counselling factors as potentially influencing the psychosocial response of disaster victims. Although posttraumatic stress disorder (PTSD) is not the only mental disorder that can develop as a result of exposure to disasters, it is probably the most frequent and debilitating psychological disorder associated with traumatic stress. In this exploratorydescriptive study the researcher aimed to explore and describe psychologists’ perceived influences of early strategies on the psychosocial response to those affected by disaster. The researcher used non-probability snowball sampling to access participants. The sample consisted of 5 participants. Semi structured interviews were conducted. Content analysis was used to analyse the data obtained from interviews. Results that emerged from the data suggest that there are many factors that influence the psychosocial response to those affected by disasters. These factors include the screening process, needs of survivors, the method of choice for treatment, the timing of intervention, pharmacology, the South African context, training and planning. The study makes a contribution to the growing knowledge of early strategies in response to those affected by disasters.
- Full Text:
- Date Issued: 2010
- Authors: Blackburn, Nerina June
- Date: 2010
- Subjects: Disasters -- Psychological aspects , Post-traumatic stress disorder , Disaster victims -- Mental health , Disasters
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9872 , http://hdl.handle.net/10948/1416 , Disasters -- Psychological aspects , Post-traumatic stress disorder , Disaster victims -- Mental health , Disasters
- Description: Currently some confusion exists as to how health professionals should best respond to the psychological needs of those affected by disasters. Some have argued that early psychological intervention is essential and others have argued that early formal psychological interventions have no useful role in post trauma response. This study highlights the importance of considering both counselling and non-counselling factors as potentially influencing the psychosocial response of disaster victims. Although posttraumatic stress disorder (PTSD) is not the only mental disorder that can develop as a result of exposure to disasters, it is probably the most frequent and debilitating psychological disorder associated with traumatic stress. In this exploratorydescriptive study the researcher aimed to explore and describe psychologists’ perceived influences of early strategies on the psychosocial response to those affected by disaster. The researcher used non-probability snowball sampling to access participants. The sample consisted of 5 participants. Semi structured interviews were conducted. Content analysis was used to analyse the data obtained from interviews. Results that emerged from the data suggest that there are many factors that influence the psychosocial response to those affected by disasters. These factors include the screening process, needs of survivors, the method of choice for treatment, the timing of intervention, pharmacology, the South African context, training and planning. The study makes a contribution to the growing knowledge of early strategies in response to those affected by disasters.
- Full Text:
- Date Issued: 2010
An analysis of factors that inhibit small and medium enterprises from exporting their products to South Africa's most important trading partners
- Muller, Franciscus Fredricus
- Authors: Muller, Franciscus Fredricus
- Date: 2003
- Subjects: Export marketing -- South Africa , Small business -- South Africa
- Language: English
- Type: Thesis , Masters , MBA
- Identifier: vital:10932 , http://hdl.handle.net/10948/197 , Export marketing -- South Africa , Small business -- South Africa
- Description: The research problem addressed in this study was concerned with the identification of factors that inhibit Small and Medium Enterprises from exporting their products to South Africa’s most important trading partners. To achieve this objective, a theoretical study was conducted to establish what literature reveals to be the most important trading partners, and the problems which businesses experience when they export their products to these destinations from the Eastern Cape. The information obtained in the literature study was analysed, and, in order to resolve the main problem, the research questionnaire was divided into four parts. • Part 1 consisted of biographical questions. • Part 2 consisted of questions aimed at establishing the reasons why organisations embarked on exporting. • Part 3 was concerned with what the respondents perceived as barriers to their export operations. • Part 4 was concerned with strategic decisions and the minimising of risk. The empirical results obtained indicate that, although inhibiting factors are a reality in exporting, these remain secondary to general market forces of supply and demand. It was shown that inhibiting factors do not play as big a role in the export process as the literature suggests.
- Full Text:
- Date Issued: 2003
- Authors: Muller, Franciscus Fredricus
- Date: 2003
- Subjects: Export marketing -- South Africa , Small business -- South Africa
- Language: English
- Type: Thesis , Masters , MBA
- Identifier: vital:10932 , http://hdl.handle.net/10948/197 , Export marketing -- South Africa , Small business -- South Africa
- Description: The research problem addressed in this study was concerned with the identification of factors that inhibit Small and Medium Enterprises from exporting their products to South Africa’s most important trading partners. To achieve this objective, a theoretical study was conducted to establish what literature reveals to be the most important trading partners, and the problems which businesses experience when they export their products to these destinations from the Eastern Cape. The information obtained in the literature study was analysed, and, in order to resolve the main problem, the research questionnaire was divided into four parts. • Part 1 consisted of biographical questions. • Part 2 consisted of questions aimed at establishing the reasons why organisations embarked on exporting. • Part 3 was concerned with what the respondents perceived as barriers to their export operations. • Part 4 was concerned with strategic decisions and the minimising of risk. The empirical results obtained indicate that, although inhibiting factors are a reality in exporting, these remain secondary to general market forces of supply and demand. It was shown that inhibiting factors do not play as big a role in the export process as the literature suggests.
- Full Text:
- Date Issued: 2003
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